Question

What is the 5th term of the geometric sequence a1=120, a2=36, a3=10.8, a6=0.2916

Answer 1

The fifth term of the geometric sequence would be 0.972

Answer 2

A geometric sequence is given by terms a₁ = 120, a₂ = 36, a₃ = 10.8, a₆ = 0.2916.

The First term is given, a = 120.

Common ratio (r) would be ratio of second term to first term i.e.

$r=\frac{a_{2}}{a_{1}} = \frac{36}{120} = 0.3$

The formula for n-th term of geometric sequence is given by as follows :-

$a_{n} =a*r^{n-1}$

It says to find 5th term of this given geometric sequence. For 5th term, n = 5.

$a_{5} =120*(0.3)^{5-1} \\\\ a_{5} =120*(0.3)^{4} \\\\ a_{5} =120*(0.0081) \\\\ a_{5} =0.972$

Hence, a₅ = 0.972 would be 5th term of the given geometric sequence.