Question

3/4, 1, 4/3, 16/9,... which of the following are recursive formulas for the nth term of the following geometric sequence?

Answer 1

nth term of geometric sequence = a(n) =
`(3/4)(4/3)^(n-1)`

Explanation:

nth term of geometric sequence = a(n)

nth term of geometric sequence = a(n) =
`ar^(n-1)`

Where,

a = first term

r = common ratio

n = number of term

So,

GP: 3/4, 1, 4/3, 16/9

a = 3/4

r = 1 / [3/4] = 4/3

n = n

nth term of geometric sequence = a(n) =
`ar^(n-1)`

nth term of geometric sequence = a(n) =
`(3/4)(4/3)^(n-1)`