Sequences And Series Ques 42

$T _r$ is always

(a) an odd number

(b) an even number

(c) a prime number

(d) a composite number

Show Answer

Answer:

Correct Answer: 42.(d)

Solution:

Formula:

An Arithmetic Progression (A.P.):

  1. $V _{r+1}-V _r=(r+1)^{3}-r^{3}-\frac{1}{2}\left[(r+1)^{2}-r^{2}\right]+\frac{1}{2}$

$ =3 r^{2}+2 r-1 $

$\therefore \quad T _r=3 r^{2}+2 r-1=(r+1)(3 r-1)$

which is a composite number.

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