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.
[tex] r=\frac{a_{2}}{a_{1}} = \frac{36}{120} = 0.3 [/tex]
The formula for n-th term of geometric sequence is given by as follows :-
[tex] a_{n} =a*r^{n-1} [/tex]
It says to find 5th term of this given geometric sequence.
For 5th term, n = 5.
[tex] a_{5} =120*(0.3)^{5-1} \\\\
a_{5} =120*(0.3)^{4} \\\\
a_{5} =120*(0.0081) \\\\
a_{5} =0.972 [/tex]
Hence, a₅ = 0.972 would be 5th term of the given geometric sequence.
