Question

How do you write a rule for the nth term of the geometric sequence and then find `a_5` given `a_3=-144, r=0.5`?

Answer 1

`a_n=-576(0.5)^(n-1),a_5=-36`

Explanation:

`"the nth term of a geometric sequence is "`

`•color(white)(x)a_n=ar^(n-1)`

`"where a is the first term and r the common ratio"`

`a_3=ar^2=-144`

`rArra=-144/(0.25)=-576larrcolor(blue)"first term"`

`rArra_n=-576(0.5)^(n-1)`

`rArra_5=-576xx(0.5)^4=-36`