Question

What is the fifth term of the geometric sequence?

a1 = 120, a2 = 36, a3 = 10.8, a6 = 0.2916

Answer 1

By looking at the sequence, i can guess that it is a division (difference is not constant).
120/36=10/3
\[\frac{ 120 }{ \frac{ 10 }{ 3 } }=36\]
\[\frac{ 36 }{ \frac{ 10 }{ 3 } }=10.8\]
\[\frac{ 10.8 }{ \frac{ 10 }{ 3 } }=0.2916\]
\[\frac{ 0.2916 }{ \frac{ 10 }{ 3 } }=0.08748\]
so the answer is 0.08748

Answer 2

a_n = a_1 * r^{n-1}
36/120 = 120/120
3/10 = r
a_6=a_n*r
10/3 .2916 = 1)5 * 3/10 * 10/3
.972 = a_5

Answer 3

36/120 = 0.3
The common ratio is 0.3
a5 * 0.3 = a6
a5 = a6/0.3 = 0.2916/0.3 = 0.972