Home
Class 12
MATHS
Let Vr denote the sum of the first r ter...

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 an AP with common difference 5

B

`Q_(1), Q_(2), Q_(3)`... are in an AP with common difference 6

C

`Q_(1), Q_(2), Q_(3)`,.... are in an AP with common difference 11

D

`Q_(1) = Q_(2) = Q_(3) = ...`

Text Solution

Verified by Experts

The correct Answer is:
B
Since, `T_(r) = 3r^(2) + 2r -1`
and `T_(r+1) = 3 (r +1)^(2) + 2(r +1) -1`
`:. Q_(r) = T_(r +1) - T_(r) = 3 [2r + 1] + 2 [1]`
`rArr Q_(r) = 6r + 5`
`rArr Q_(r +1) = 6(r +1) + 5`
Common difference `= Q_(r +1) - Q_(r) = 6`
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 .The sum V1+V2+...+Vn is

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 is always (A) an odd number (B) an even number (C) a prime number (D) a composite number

If (r+1)t h term is the first negative term in the expansion of (1+x)^(7//2), then find the value of rdot

If T , denotes the r^(th) term in the expansion of [x + 1/x]^(23) , then

if (m+1)th, (n+1)th and (r+1)th term of an AP are in GP.and m, n and r in HP. . find the ratio of first term of A.P to its common difference

Write three terms of the GP when the first term 'a' and the common ratio 'r' are given? (i) a=4, r=3 (ii) a=sqrt(5), r=1/5 (iii) a= 81, r=-1/3 , (iv) a= 1/64, r=2

In an infinite geometric series the first term is a and common ratio is r . If the sum of the series is 4 and the seond term is 3/4 , then (a, r) is

If the coefficients of the (2r+4)t h ,(r-2)t h term in the expansion of (1+x)^(18) are equal, then the value of r is.

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

In a geometric series , the first term is a and common ratio is r. If S_n denotes the sum of the n terms and U_n=Sigma_(n=1)^(n) S_n , then rS_n+(1-r)U_n equals