Question

Which term of the sequence { 16/9, 4/3, 1, 3/4 ... } is 243/1024?

Answer 1

The `8`th

Explanation:

This is a geometric sequence with initial term `16/9` and common ratio `3/4`.

The general term of the sequence can be written:

`a_n = 16/9 * (3/4)^(n-1) = (3/4)^(n-3)` for `n = 1, 2, 3,...`

Observe that `243 = 3^5` and `1024 = 2^10 = 4^5`.

Comparing this power with the expression `n - 3`, we find that:

`a_8=243/1024`.