Question

Write a rule for the geometric sequence with the given description

Answer 1

a.
`a_n = -3(5^(n - 1))`

b.
`a_n = 72(3^(1 - n))`

Explanation:

a.

`a_1 = -3`

`a_2 = -3(5^1)`

`a_3 = -3(5^2)`

Notice that in each term, the exponent of the 5 is 1 less than the term number.

The general term is

`a_n = -3(5^(n - 1))`

b.

`a_1 = 72`

`a_2 = 72((1)/(3))^1`

`a_3 = 72((1)/(3))^2`

Notice that in each term, the exponent of the 1/3 is 1 less than the term number.

The general term is

`a_n = 72((1)/(3))^(n - 1)`

`a_n = 72((1)/(3^(n - 1)))`

`a_n = 72(3^(1 - n))`