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

A

an odd numbeer

B

an even number

C

a prime number

D

a composite number

Text Solution

Verified by Experts

The correct Answer is:
D
`V_(r +1) - V_(r) = (r +1)^(3) -r^(3) - (1)/(2) [(r + 1)^(2) - r^(2)] + (1)/(2)`
`= 3r^(2) + 2r -1`
`:. T_(r) = 3r^(2) + 2r -1 = (r + 1) (3r -1)`
Which is a composite number
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