Question

Calculate the 5th term of the sequence which has this explicit formula: an=3/2n(2n+5), n=1,2,...

A. 63/64
B. 39/8
C. 17/4
D. 9/2

Answer 1

D. 9 ÷ 2

Explanation:

For getting the nth value of the sequence we simply put the value of n in a formula.

In the given sequence for finding the 5th term we simply put n = 5 in given explicit formula:

We have
`a_(n) = (3)/(2n)(2n+5)`

Putting n = 5

`a_(5) = (3)/(2*5)(2*5+5)`

⇒
`a_(5) = (3)/(10)(15)`

⇒
`a_(5) = (9)/(2)`

Thus, option (D) is correct.