What is the fifth term of the geometric sequence a1=120, a2=36, a3=10.8, a6=0.2916?

First we need to find the common ratio by dividing the second term by the first term. 36/120 = 3/10

an = a1 * r^ (n-1)

n = term to find = 5

a1 = first term = 120

r = common ratio = 3/10

now we sub and solve

a5 = 120 * 3/10^ (5 - 1)

a5 = 120 * 3/10^4

a5 = 120 *.0081

a5 = 0.972 < = = = fifth term

or we could have just done this ... since we multiply by 3/10 to find the next number ...

a3 = 10.8 ... 10.8 * 3/10 = 3.24 < = = 4th term

3.24 * 3/10 = 0.972 < = = fifth term

The formula for geometric sequence is an = a1 r^ (n-1) where r is the geometric factor and n is an interger. In the sequence given, r is equal to 3/10. In this case, an = 120 * (3/10) ^ (n-1). Solving for a5, a5 = 120 * (3/10) ^ (5-1) = 0.972