# 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#?

##### 1 Answer

Dec 15, 2017

#### 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#