SATHEE: Sequences and Series 2 Question 12

Sequences and Series 2 Question 12

13.

$T_{r}$ is always

(a) an odd number

(b) an even number

(d) a composite number

Show Answer

Answer:

Correct Answer: 13. (d)

Solution:

$V_{r + 1} - V_{r} = (r + 1)^{3} - r^{3} - \frac{1}{2} [(r + 1)^{2} - r^{2}] + \frac{1}{2}$

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

$∴ T_{r} = 3 r^{2} + 2 r - 1 = (r + 1) (3 r - 1)$

which is a composite number.

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Sequences and Series 2 Question 12

13.

Answer:

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