Question

The explicit formula for the geometric sequence 10,30,90,180

Answer 1

nth term = 10(3)^(n-1).

Explanation:

General form is a1 r^(n-1) where a1 is the first term and r is the common ratio and n is the term number.

For this sequence a1 = 10 and r = 30/10 = 3.

The explicit formula is nth term = 10(3)^(n-1)

Answer 2

`a_(n)` = 10
`(3)^(n-1)`

Explanation:

The n th term of a geometric sequence is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

Here a = 10 and r = 30 ÷ 10 = 3, thus

`a_(n)` = 10
`(3)^(n-1)`