Home
Class 11
MATHS
Let the sequence a1, a2, a3,...............

Let the sequence `a_1, a_2, a_3,.............a_(2n)` form an A.P. Then`a_1^2-a_2^2+a_3^2- ......+a_(2n-1)^2 - a_(2n)^2=`

A

`(n)/(2n-1)(a_1^2-a_(2n)^2)`

B

`(2n)/(n-1)(a_(2n)^2-a_(1)^2)`

C

`(n)/(n+1)(a_(1)^2+a_(2n)^2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequencea_1,a_2....a_n form and AP. Then a_1^1-a_2^2+a_3^2-a_4^2... is equal to

Let (a_1,a_2,a_3....a_4) be a permutation of (1,2,3....n) for which a_1 > a_2 .a_3 >.........> a_ (a/2) and a_(n/2=1) a_2 >a_3..........>a_((x-2)/2 and a_((n-1)/2 <.... < a_2for n as positive integers. Let the total number of permutation of n be p(n). if 200 < p(n) < 5000. then values of n is /are

If a_(n) = n(n!) , then what is a_1 +a_2 +a_3 +......+ a_(10) equal to ?

Given that (1+x+x^2)^n=a_0+a_1x+a_2x^2+.....+a_(2n)x^(2n) find i) a_0 + a_1 +a_2 .. . . .+ a_(2n) ii) a_0 - a_1 + a_2 - a_3 . . . . + a_(2n) iii) (a_0)^2 - (a_1)^2 . . . . .+ (a_(2n))^2

If the nonzero numbers a_1,a_2,a_3,....,a_n are in AP, prove that 1/(a_1a_2a_3)+1/(a_2a_3a_4)+...+1/(a_(n-2)a_(n-1)a_n)=1/(2(a_2-a_1))(1/(a_1a_2)-1/(a_(n-1)a_n)) .