Home
Class 12
MATHS
Let V(r) denote the sum of the first r t...

Let `V(r)` denote the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common difference is `(2r-1). Let `T(r)=V(r+1)-V(r)-2 and Q(r) =T(r+1)-T(r) for r=1,2` Which one of the following is a correct statement? (A) `Q_1, Q_2, Q_3…………..,` are in A.P. with common difference 5 (B) `Q_1, Q_2, Q_3…………..,` are in A.P. with common difference 6 (C) `Q_1, Q_2, Q_3…………..,` are in A.P. with common difference 11 (D) `Q_1=Q_2=Q_3`

Promotional Banner

Similar Questions

Explore conceptually related problems

Let V_r denote the sum of the first r terms of an arithmetic progression (AP) whose first term is r and the common difference is (2r-1). Let T_r=V_(r+1)-V_r-2 and Q_r =T_(r+1)-T_r for r=1,2 T_r is always (A) an odd number (B) an even number (C) a prime number (D) a composite num,ber

If the sum of the first 4 terms of an arithmetic progression is p, the sum of the first 8 terms is q and the sum of the first 12 terms is r, express 3p+r in terms of q.

If S_n=n P+(n(n-1))/2Q ,w h e r eS_n denotes the sum of the first n terms of an A.P., then find the common difference.

If S_n=n P+(n(n-1))/2Q ,w h e r eS_n denotes the sum of the first n terms of an A.P., then find the common difference.

If S_n=n P+(n(n-1))/2Q ,w h e r eS_n denotes the sum of the first n terms of an A.P., then find the common difference.

Let T_r be the rth term of an A.P. whose first term is -1/2 and common difference is 1, then sum_(r=1)^n sqrt(1+ T_r T_(r+1) T_(r+2) T_(r+3))

The common difference of the A.P. is 1/(2q),(1-2q)/(2q),(1-4q)/(2q),\ dot is (a)-1 (b) 1 (c) q (d) 2q

If the pth, qth, and rth terms of an A.P. are in G.P., then the common ratio of the G.P. is a. (p r)/(q^2) b. r/p c. (q+r)/(p+q) d. (q-r)/(p-q)

The sums of first p, q, r terms of an A.P. are a, b, c respectively. Prove that (a)/(p) (q-r) +(b)/(q) (r-p) +(c )/(r) (p-q) =0

If a_(1),a_(2),a_(3),…. are in A.P., then a_(p),a_(q),a_(r) are in A.P. if p,q,r are in