Sequences and Series 2 Question 12
13. $T _r$ is always
(a) an odd number
(b) an even number
(c) a prime number
(d) a composite number
Show Answer
Answer:
Correct Answer: 13. (3050)
Solution:
- $V _{r+1}-V _r=(r+1)^{3}-r^{3}-\frac{1}{2}\left[(r+1)^{2}-r^{2}\right]+\frac{1}{2}$
$$ =3 r^{2}+2 r-1 $$
$\therefore \quad T _r=3 r^{2}+2 r-1=(r+1)(3 r-1)$
which is a composite number.
