Sequence & Series 02 | Arithmetic Progression ( A.P. ) | JEE | CLASS 11 | PACE SERIES
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AT 44:10 the correct ans is n2d/2 - nd/2 + na (b'coz 2a and (n-1)d are two diffrent terms and thus u have to multiply n/2 with both seperatly )
You are right bro but no reply from respectible sir
Yes you are right even I thought this
same here bro i also thought this
Yes u r right and by solving it we will get
2Sn = n2d-nd+2an
This video is 3 years old still helping students for preparation oF JEE
Physics wallah sir is spreading his army...
RESPECT++
❤❤❤❤❤++
@Kashyap Singhmtlb views paane k liye kuchh bhi karoge😠
ua-cam.com/video/GvMtPtnQGdA/v-deo.html Alakh Sir on Hud Hud Dabangg 😂😂😂😂
@@akshay_anand360 ua-cam.com/video/GvMtPtnQGdA/v-deo.html Alakh Sir on Hud Hud Dabangg 😂😂😂😂
2019 MISSION
PASSED
RESPECT+
🤟👌
homework answer 55:50 :
we can make pairs of consecutive terms in sequence
(1^2 - 2^2) + (3^2 -4^2)...............(99^2-100^2)
this will give -3 -7 -11 -15 .. . . . . -199
as this is an ap so its sum is -5050
-4^2 = 16 not -16
-2298
babby thats wrong
yes bhai
@@shreyanmohapatra1511 you are wrong. - square se bahar h.
I just donno what would I do without this teacher ❤️ please continue these sir
he has left physics wallah months ago
@@aaravbhardwaj261 why
Best teacher and teaching method makes maths a fun in learning
46:20
Yes sir, ab tak ka samajh aa gaya hai ekdam bhannat tariké Se
At first it seemed like Alakh Pandey(A.P.) Sir's graph of greatness🙏
Same bro❤️
His graph is not A.P, it's G.P.
No bro, that graph is Exponentially increasing 😘😎
@@AAhamed007 GP means great person?
@@shivamarora2969 arre Yaar😂😂....... It means Geometric Progression... Where instead of constant adding you constantly multiply... I hope you get the difference 🙂
the visualization which he gave for sum of odd numbers was nxt level
Aman sir is looking like Great Mathematician Ramanujan in his fancy moustache.🔥🙏🏻
Yes👍❤❤
Yeah
ua-cam.com/video/2QwXonW_Bs0/v-deo.html
ua-cam.com/video/GvMtPtnQGdA/v-deo.html Alakh Sir on Hud Hud Dabangg 😂😂😂😂
@@sanamaryam690 ua-cam.com/video/GvMtPtnQGdA/v-deo.html Alakh Sir on Hud Hud Dabangg 😂😂😂😂
When the sum of first n terms of an A.P.'s formula is given in form of quadratic equation in terms of n then it's common difference = 2(coefficient of n²). Hope guys it will help you.
ua-cam.com/video/eedlES1B8iM/v-deo.html
Thanks
And first term (a) is the sum of coefficients of n^2 and n
Sir samjo ki 63 ka nikalna hai
To ksze
Arithmetic progression is looking very easy because you Aman sir.😊😊
Awesome , understand each Nd every concept related to this session 👍👍👍
How interactive sir's lecture is!!! 👍👍👍👍👍👍👍👍👍👍
46:00 Sir answer is
S = [5n² - 7n]/4
❤️❤️
Bhai n(5n-7)/4
Aage expand karge toh wahi aayega na 5n²-7n/4
At 44:10 as n/2 [2a + (n-1)d], here 2a & (n-1)d both are different terms then it will be an + n²d/2 + nd/2 and further simplified. 🤖
Exactly mei bhi itni deerr sei yahi soch raha tha 🤝
I too confused on this time
Cutie pie question
Answer: -5050
Can you explain it bro!
@@ShivamKumar_077 bro take a²-b² formula from start and ending you will get the result
44:46
Sir it shouldn't be : n²d-nd-an
It should be : (n²d-nd+2an) / 2
Fhir sir ne pehle hi 2 ko divide kue kiye
Nic Bro bit sir just want to convey that it's a quadratic expression.
@@Abdul_36638 bhai sir ne 2 ko divide kiya jisse 2a ka 2 cancel ho gaya
But sir ka dhyan nahi hoga aur sir ne (n-1)d ko divide nahi kiya jo ki ultimately sir ke equation ke according --- n²d/2 - nd +na ho jata
sum of roots taken 2 at a time is _b/a
yes you are right but when the quadratic equation is divided by 2 , which is constant is doesn't matter and dosent change the power of the quadratic equation.
Amazing... Description of arithmatic progression .... Which gives me knowledge and be knowledgble
46:23 yes sir all the concepts are clear ❤️
Ya bro
In the first n even no.
2+4+6+8.........2n
2(1+2+3+4......n) = 2[n/2(n+1)]
=n(n+1)
H.w question is an decreasing A P
First term = -3
Last term = -199
Total no. Of terms =50
SUM= -5050
(Common difference =-4)
I thought that I was starting CARRYMINATI's video
🤣🤣🤣
To kaise he aap log👍👍
Shi entry thi sir ki 😂😂😂
Sir poora samagh main aa gya thanks sir😁😉
And by the way nice moustache.
Sir Aap or Pandey sir ek dam BHANNAAT GANG
Missing those "Note kr liya mitar de" , "Copy or pen nikal lo or chuha khana band kro" , "Turram Turram turr turrr😂😂" .
😂
👌👌👌👌
🤣
Bro dil ki baat boldi tune 🙌🙌🙌
True
Respected sir
The answer of the last homework question is -5050,by taking 1^2-2^2 as one term. n term is 50, a is -3, difference is -4 .I am studying in 8 standard learning 11 physics and maths from physics wallah ,really awesome teaching
Aur bahi
Thankyou sir.. for this nice lecture..
46:20 yes sir ekdum ache se smjh aa gya
29:10 very nice explanation done practically thanks
PHYSICS WALLAH(at door) : Knock knock 😎
VEDANTU : Kon aaya hai.🤔
UNACADEMY : Mai dekhta hu🙄
PHYSICS WALLAH : TERA BAAP AAYA😈😈
@@jiteshbansal4145 yeah bro
But that was just for fun and for appreciating our faculties😎😎
@@hostelers18 o bhai bhai 😂😂😂😂
@@akshay_anand360 😅😅😅
*Homework answer*
Given series is 1²-2²+3²-4²+....100 terms
By grouping the terms,we get
(1²-2²)+(3²-4²)+(5²-6²)+..... upto 50 terms
(1-4)+(9-16)+(25-36)+.... upto 50 terms
(-3(+(-7)+(-11)+..... upto 50 terms
Since we can see that, this is an A.P
Here,a=-3,d=-7-(-3)=-4,n=50
S=50/2[2×(-3)+49×(-4)]
S=-5050
Shayad sahi h sir☹️😅😅
Yes -5050 I also got
I too
same answer i got
may I pls know why you grouped and how it became upto 50 terms please
@@OmNamahShivaya810 See friend , The given AP is 1²-2²+3²-4²+....100 terms
You make pairs of Two numbers
for example ( 1²-2²) and (3²-4²) till ....100 terms
So you will end up to 50 pairs , and let first term be (1²-2²)
after solving you get common difference as (-4) and then put the valuse in the formula [Sn = n/2{2a +(n-1)d}]
and you get the answer which is *-5050*
6:39 Agar aman sir ko math me laga daala to life jhingaalaala 😆😆😆😅😂😂😂🤣🤣🤣
Hula lala 😂😂😂🤣🤣🤣 didi
🤣🤣🤣
Are yaar tum teeno hamesha mujhe ek hi comment dikh jata ho😁
@@commentmatkrpadhaikr9922 We are brothers and sisters
@@pratikgoswamiiitbombay8767 yes 🥰☺🤗🤗
46:14 sir sb ek dm bhannaaatt tareeke se samajh aa gya ap tension na lo.🥰😀.
Bilkul 🥰
Sir anwer of cutipie question is -5050 here's the explanation
drive.google.com/file/d/1yKMeAHi_x73lkeDnUSUZsQs_HRjGowDX/view?usp=drivesdk
Thanks sir😊
Kon kon 2x ki speed pe dekh raha hai😂
sir all properties and all about A.P is clear
🙏🙏🔥💥Let's request Alakh Sir and his team for 🔥Accelerate🔥batch 2021for PCM students for IIT JEE 2022🙏🙏💥🔥🙏🙏
Shi hai bhai
Yes
Mail kro
Yes sir plzzzzzzzzzzzzzzzzzzzzzzzzzzz
Yes.......but 2 year course for jee 2023 also
Thank you so much sir 🙏🏻🤗😎
hw que : -50
1²+3²+5² ------------ 99² is sum of 1st 50 odd no.s i.e n²=2500
-(2²+4²+6²------------- 100²) is the sum of 1st 50 even no.s i.e n(n+1) = -2550
Their sum= -50
sir apki videos me hi mujhe sabse jada maja ata hai after alakh pandey sir, alakh sir hamesha padhate waht hum logo ka dhyen khich lete hai focus karne ke liye and sir aap dhyan bhatane nhi dete "tujhse baat kar raha"," i know tumhe meri baat samajh me arahi hai"," yaha dhyan do"sir mujhe apki ye line badi achi lagti hai sir iske wajah se mera focus bana rehta hai and aisa feel hi nhi hota ki ye ek recorded session hai hamesha lagta hai ki live and aap muhi se baat kar rahe hai
Answer of homework question= -5050😊😊😊😊😊
Please check the six terms in A.P 🙏
Also bro at 49:40 sir takes -D/a in product of roots whereas it was c/a??
*I just got goosebumps at the starting 😂*
ua-cam.com/video/kanKMEiMXX8/v-deo.html
@@chhagansuthar2956 sahi batt bro😂
@@arpitaadideo4852 😉😘
Using formula (a^2 --b^2) = (a-b) (a+b )
(1-2)(1+2) + (3-4)(3+4) + (5-6)(5+6) ......+ (99-100)(99+100)
-1(3) - (7) - (11) ......- 199
Taking -1 as common
-1 ( 3+7+11+.....199)
Then Sn = - 5050
Hence solved BhannatlY
😊😊😊😊
Good
आपके जैसा आसान maths पढाना सबके बस की बात नहीं होती।
Very very thank you sir
Sir in points no 8 . You not divide by 2 in (n²-n)d 44:23
Bilkul main bh yahan confuse hua
55:30 the answer is -5050
Kaise aya can you please help me
mera to -2550 aa raha ahi
aapka kese aaya???
can you explen me
plz......
From were u brings such great teachers alakh sir
Yes
Earth
Sir in the Sn find ques if we let three terms of A. P be (a-d),a, (a+d) then we easily calculated the value of Sn sir apne hi to padaya tha before lecture me
But bro usme toh answer different aa rhaa h
Best teacher for class 11 maths on you tube.
Check property 8 , "dn^2-nd-an" or "na+(dn^2-dn)/2" is true check property numbre 8 again
40:46 Sir ji ' a-3d ' miss hogya
Yes
Don't teach teacher
40:54
Sir here we to have write 6 terms but you have only mentioned 5terms .
In this a-3d will also come after a-5d
Hii
Nice 😍
Aman sir is unique mathematician...
Mai vi west bengal ka youngest mathametician hu😊
@@arnabstudy professor Neena gupta ma'am hai😅
46:12 Sir ekdum mast samajh mein aaya hai
At 44:10 It Is (+a.n)
Sir my answer is -5050 :)
Due to your great teaching I can solve these question while being in 9th
BRO 6TH STANDARD STUDENT HERE
I just born now, I am here now (•‿•)
@@grinjow4u hello from heaven 😌
Bro 7th student
Mai to kg 1 me hu
46:18 i UNDERSTOOD EVERYTHING SIR.... NO DOUBTS
40:45 here it is a-3d
Yes sir all the concepts are clear....
****HW****
1. take first two terms and form an AP __ -3 , -7 ,-11...... ( we can observe that "d= -4" , "a= -3)
2. now that we have took two terms to form an AP , so we have 50 terms now
3. find S^50 to evaluate the first 50 terms we just made and the resulting solution must be *-5050*
"25(-202)"
Sum = -404 / 404
Sir your teaching is just amazing.
1²-2²=-3. 3²-4²=-7. And so on
-(3+7+11……… upto 50 terms)
=-[50/2(2*3+49*4)]
=-5050
DONE BHANNATLY
Bhannat bhai. Mere se pehli baar me Nani bana tha
Correct answer
Yess
Your teaching style is amazing sir ❤❤❤❤❤🙏🙏🙏🙏🙏
Sir the answer of Homework Question is = 171700
At last i applied n(n+1)(n+2)/6 and the answer came..!!!
@Amit Kumar bro it will be -5050
Iss safar main sab samajh main aa gaya sir bhannatly!!
answer of the question is -5050
I don't understand the first que little bit only
The part that I don't understand was that how has taken cube roots of some please help me to understand
AT TIME STAMP -48:37
Dekho it is given in the question that first three terms of an AP are the roots of cubic expression
Toh let a be first term of that AP with common diff d
So next terms will be
a+d and a+2d
Uske baad we know that
For ax^3+bx^2+cx+d= 0
sum of roots in cubic = -b/a
And product of roots= c/a
Toh yaha par b= -24, c= 23
And a= 4( don't get confused with first term of AP jo sir aur mene yaha par liya dono alag alag hai )
Uske baad bus sum and product kardo
a, a+d and a+2d ka 👍
@@prt4691 may I ask detail of yours
By the way thanks a lot for helping once again
Welcome alakh sir to Delhi ❤️❤️
Thank you sir🙏🏻🙏🏻🙏🏻
Starts 1:34
Sum of n terms of an AP 7:24
Sum of first N-natural numbers 19:44
Sum of First Even & Odd 21:40
Properties of an AP 29:54
Thanks yr
Thanks bro
Thanks bro
thnx 👍
Cutie pie ans. =-5050 I did it by formula (a-b)(a+b)=a^2-b^2
46:20 .. YES BHANNAT SAMAJ AA RAHA HAI JIII .... EKDAM MAST
56:05 answer is -5050
First answer☝
true
Bro n ki value kya leni h ???
@@sarojmishra5644 100
Mindblowing sir ji
PHYSICS wall change poor family and provide good quality education thanks sir 🙏🙏🙏🙏🏼 🙏🙏🙏 🙏🏼🙏🏼🙏🏼🙏🏼🙏🏼🙏🏼🙏🏼
Sir I think 8th property is not correct
I think
an +( dn² - dn ) /2
Is correct
Sir please 🙏🙏🙏clear my doubt
U r absolutely right ny child rama will bless you
29:06 kya smjhaya sir aapne, bhannat tareeke se smjh aa gyaaa !!!!!
Sir plz make a lecture on mathmateical reasoning for jee 2021 plz sir plz 🙏🙏🙏🙏🙏🙏🙏
Wao sir aap great ho ji
Sir aapka padhane ka tarika bhannnnnnnnnat hai
Who is in 2024😂😂
😅🙋
Tera baap
Me
🙋
😂😂😂
In that quadratic equation that formed, it will be +9 na when it comes to left side
Best explanation ever sir ...thank you so much sir 👍👍👏👏
H. W cutiepie question
Ans.... - Guass sum = - 5050
ua-cam.com/video/eedlES1B8iM/v-deo.html
Sir I understood btw super explanation
No booring
44:12 Sir idhar (n-1)d ko bhi 2 se divide karna haina??
Wahi to mai bhi soch raha hoon poori eqn addition mein hain to poore se divide hoga lekin khali 2 Kaat diya
Waha sir se toda mistake ho gaya
(n-1)d/2 aayega 👍
Good night
46:04 sir last wale question m a=2 and d=5/2 se bhi sattisfy hora h
agar hum roots ko a-d , a , a+d lenge toh
Question me bola gya hai first 3 term
@@letslearn1086 😉😘❣️
55:48 ans
To find the sum of the given series:
1
2
−
2
2
+
3
2
−
4
2
+
…
+
9
9
2
−
10
0
2
1
2
−2
2
+3
2
−4
2
+…+99
2
−100
2
We can see that this is an alternating series where each term alternates between addition and subtraction.
1
2
−
2
2
+
3
2
−
4
2
+
…
+
9
9
2
−
10
0
2
=
(
1
2
−
2
2
)
+
(
3
2
−
4
2
)
+
…
+
(
9
9
2
−
10
0
2
)
1
2
−2
2
+3
2
−4
2
+…+99
2
−100
2
=(1
2
−2
2
)+(3
2
−4
2
)+…+(99
2
−100
2
)
We can also see that each pair of terms can be represented as the difference of consecutive squares:
1
2
−
2
2
=
(
1
−
2
)
(
1
+
2
)
=
−
3
1
2
−2
2
=(1−2)(1+2)=−3
3
2
−
4
2
=
(
3
−
4
)
(
3
+
4
)
=
−
7
3
2
−4
2
=(3−4)(3+4)=−7
…
…
9
9
2
−
10
0
2
=
(
99
−
100
)
(
99
+
100
)
=
−
199
99
2
−100
2
=(99−100)(99+100)=−199
So, the sum of the given series is the sum of these differences:
(
−
3
)
+
(
−
7
)
+
…
+
(
−
199
)
(−3)+(−7)+…+(−199)
This is an arithmetic series with the first term
�
=
−
3
a=−3, the last term
�
=
−
199
l=−199, and the common difference
�
=
−
4
d=−4 (since each term decreases by 4).
We can use the formula for the sum of an arithmetic series:
�
�
=
�
2
(
�
+
�
)
S
n
=
2
n
(a+l)
Where
�
�
S
n
is the sum of the series,
�
n is the number of terms,
�
a is the first term, and
�
l is the last term.
Now, to find
�
n, we use the formula for the nth term of an arithmetic series:
�
=
�
+
(
�
−
1
)
�
l=a+(n−1)d
Substituting the known values:
−
199
=
−
3
+
(
�
−
1
)
(
−
4
)
−199=−3+(n−1)(−4)
Solving for
�
n:
�
−
1
=
−
199
+
3
−
4
n−1=
−4
−199+3
�
−
1
=
−
196
−
4
n−1=
−4
−196
�
−
1
=
49
n−1=49
�
=
50
n=50
Now, plugging
�
=
50
n=50,
�
=
−
3
a=−3, and
�
=
−
199
l=−199 into the sum formula:
�
50
=
50
2
(
−
3
−
199
)
S
50
=
2
50
(−3−199)
�
50
=
25
(
−
202
)
S
50
=25(−202)
�
50
=
−
5050
S
50
=−5050
So, the sum of the series is
−
5050
−5050.
am i the only one who noticed that the thumbnail has changed
No me too
True
Me too
Me too bro
Mee too noticed, but not commented 😂😂🤣🤣
46:20 yes sirr
🤗
Sir pls ek video bana dijiye books par for jee mains and advance🙏🙏🙏🙏🙏❤️
Cengage publications for Jee Advanced
Arihant publications for Jee Main
@@globetroter6882 but I think arihant is best for JEE mains as well as for JEE Advanced (All 7 parts)......
-5050 ans. Of last question
Bro n ki value kya leni h ???
@@sarojmishra5644 n ki value 50 leni hai
HW question...
1^2 - 2^2 +3^2 - 4^2+.........+98^2 -100^2
We can do that
1^2 -2^2=(1-2)(1+2)=-3
Similarly
3^2-4^2= -7
We will get an AP of 50 terms
I.e. -3,-7,-11,............-195,-199
We get a=-3, d=-4 and n=50
Now sum=
50/2[2(-3) +(50-1)(-4)]
= 25[-6 -196]
=25[-202]
= -5050
Sir thodi bahot time lag gyi solve Karne me but ban gyi
Please bataiyega Sahi hai ya nhi❤️❤️❤️
13:07 Sir what do you mean by khula bhaitne ki aadat hai....🤭🤭
G.O.A.T (greatest of all time )
teacher of India 🇮🇳 aman sir. This is my feelings from my heart if anybody have the same feeling for Aman sir please hit the like button
Now not. !! 😭😭
Answer of the last question = -5050
Sir kya jee 2022 ke lie course start hoga? Sir please reply otherwise we will have to join offline coaching.
Aur jiska bhi ye same question hai wo like kre
👇
Arree this course is for jee 2022 ree
Yes sir please tell
@@atharvpatil1838 this course is for 11th we need for 12th also
Start Pace series for 12th class also