The sum of the series a-(a+d)+(a+2d)-(a+...

The sum of the series `a-(a+d)+(a+2d)-(a+3d)+...` up to `(2n+1)` terms is: a. `-n d`. b. `a+2n d`. c. `a+n d`. d. `2n d`

`a^(2)+3nd^(2)`

`a^(2)+2nad+n(n-1)d^(2)`

`a^(2)+nad+n(n-1)d^(2)`

`a^(2)+2nad+n(2n+1)d^(2)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

SEQUENCES AND SERIES
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|129 Videos
QUADRATIC EXPRESSIONS AND EQUATIONS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|50 Videos
SETS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n-1/2(3^(-n)-1) (b) n-1/2(1-3^(-n)) (c) n+1/2(3^n-1) (d) n-1/2(3^n-1)

If the sum of n terms of an A.P. is 2n^2+5n ,\ then its nth term is a. 4n-3 b. 3n-4 c. 4n+3 d. 3n+4

The mean deviation of the series a , a+d , a+2d ,.....,a+2n from its mean is (a) ((n+1)d)/(2n+1) (b) (n d)/(2n+1) (c) (n(n+1)d)/(2n+1) (d) ((2n+1)d)/(n(n+1))

The mean deviation of the series a , a+d , a+2d , , a+2n from its mean is ((n+1)d)/(2n+1) (b) (n d)/(2n+1) (c) (n(n+1)d)/(2n+1) (d) ((2n+1)d)/(n(n+1))

Statement-1: The sum of n terms of the series a+(a+d)+(a+2d)+...(a+(n-1)d)=(n)/(2)[2a+(n-1)d] Statement-2:- Mathematical induction is valid only for natural numbers.

The sum of first n odd natural numbers is 2n-1 (b) 2n+1 (c) n^2 (d) n^2-1

The sum to infinity of the series 1+2(1-(1)/(n))+3(1-(1)/(n))^(2)+ . . .. . . . , is (A) n^(2) (B) n(n+1) (C) n(1+(1)/(n))^(2) (D)None of these

In an A.P. with first term 'a' and the common difference d(a, d!= 0) , the ratio 'rho' of the sum of the first n terms to sum of n terms succedding them does not depend on n . Then the ratio (a)/(d) and the ratio 'rho' , respectively are

(lim)_(n->oo)(n !)/((n+1)!+n !) is equal to a. 1 b . 0 c. 2 d. 1/2

If S_n denote the sum of n terms of an A.P. with first term a and common difference d such that (S_x)/(S_(k x)) is independent of x , then (a) d=a (b) d=2a (c) a=2d (d) d=-a

OBJECTIVE RD SHARMA ENGLISH-SEQUENCES AND SERIES-Chapter Test

The sum of the integers from 1 to 100 which are not divisible by 3 or ...
Text Solution
|
Let the harmonic mean and geometric mean of two positive numbers be in...
Text Solution
|
The sum of the series 1 + 2.2+ 3.2^(2) + 4.2^(3) + 5.2^(4) + ….. +...
Text Solution
|
If a\ (1/b+1/c),\ b(1/c+1/a),\ c(1/a+1/b) are in A.P. prove that a ,\ ...
Text Solution
|
If the m^(th),n^(th)andp^(th) terms of an A.P. and G.P. be equal and b...
Text Solution
|
The 7th term of a H.P. is (1)/(10) and 12 th term is (1)/(25), find th...
Text Solution
|
The length of side of a square is 'a' metre. A second square is formed...
Text Solution
|
The harmonic mean of the roots of the equation (5+sqrt(2))x^2-(4+sqrt(...
Text Solution
|
If three positive real numbers a,b,c, (cgta) are in H.P., then log(a+c...
Text Solution
|
In an A.P., the p^(th) term is 1/q and the q^(th) term is 1/p. fin...
Text Solution
|
The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n...
Text Solution
|
If a,b,c are in H.P. , then
Text Solution
|
The odd value of n for which 704+1/2(704)+… upto n terms = 1984-1/2(1...
Text Solution
|
The positive interger n for which 2xx2^2+3xx 2^3+4xx2^4+….+nxx2^4=2^(n...
Text Solution
|
If 1^2+2^2+3^2++2003^2=(2003)(4007)(334) and (1)(2003)+(2)(2002)+(3)(2...
Text Solution
|
The sum to n terms of the series (n^(2)-1^(2))+2(n^(2)-2^(2))+3(n^(2...
Text Solution
|
The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...
Text Solution
|
If Hn=1+1/2+...+1/ndot , then the value of Sn=1+3/2+5/3+...+(99)/(50) ...
Text Solution
|
Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+............
Text Solution
|
If a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+(1)/(5)+ . . . .+(1)/(2^(n)-1), then
Text Solution
|