Question

Calculate a5 for the geometric sequence in which a1=8 and the common ratio is 1.5.

Answer 1

`\boxed{a_5 = 40.5}`

Explanation:

Common ratio r of a geometric sequence is the ratio of each term to the previous term and is a constant

Thus if you have a sequence a₁, a₂, a₃, a,...

`r = (a_2)/(a_1) = (a_3)/(a_2) = (a_4)/(a_3) \cdots`

For a geometric sequence with common ratio
`r` and a starting value of
`a_1`the nth term is given by the formula:

`a_n = a_1r^(n-1)`

Here
`a_1 = 8, r = 1.5`

and we are asked to find the 5th term

`a_5 = 8 * 1.5^((5-1))\\\\= 8 * 1.5^4\\\\=40.5\\\\`ANSWER

The terms of the sequence are
8, 12, 18, 27, 40.5 with 8 being the first term and 40.5 the 5th term