Question

How do you find a formula of the nth term for this sequence: 8/9,1,9/8,81/64?

Answer 1

The nth term of the given series is `(9/8)^(n-2)`

Explanation:

In the sequence: `{8/9, 1, 9/8, 81/64, .........}` the ratio of a term to its preceding term is `9/8`, Hence it is a geometric sequence.

In a geometric sequence, if `a` is the first term and ratio of a term with its preceding term is `r`, nth term is given by `a.r^(n-1)`.

Hence nth term of the given series is `(8/9)*(9/8)^(n-1)` or `(9/8)^(n-2)`