Question

Find the 8th term of the sequence whose common ratio is 1/3 and whose first term is 3

Answer 1

The 8th term is
`(1)/(729)`.

Explanation:

Let's begin with the formula for a geometric sequence. We know this is geometric because we are working with a common ratio, or the number we multiply to find each term.

`a_n=a_0(r)^(n-1)`

In this formula,
`a_0` is the first term,
`r` is the common ratio, and
`n` is the desired term. We know the values of
`r`,
`a_0`, and
`n` from the given information:

`a_0=3\\r=(1)/(3)\\n=8`

Substituting those values we get:

`a_8=3((1)/(3))^(8-1)`

`a_8=3((1)/(3))^7\\a_8=3((1)/(2187))\\a_8=(3)/(2187)\\a_8=(1)/(729)`