Question

What is the 10th term of the geometric sequence 3, 12, 48, …?

Answer 1

The `10`th term is `786432`

Explanation:

A geometric sequence is a sequence of the form
`a, ar, ar^2, ar^3, ...`
where `a` is an initial value and `r` is a common factor between terms.

Looking at this, we can tell that the `n`th term will be of the form `ar^(n-1)` and so the `10`th term will be `ar^9`.

In the given sequence, we start at `3` and thus `a=3`.

To find `r` we need only divide a term by the term prior to it. So, for example, dividing the second term by the first gives us

`r = (ar)/a = 12/3 = 4`

Thus the `10`th term is `3*4^9 = 786432`