Answer:
The explicit formula for the nth term of the sequence is \(a_n=0.75(6)^{n-1}\).
Step-by-step explanation:
The recursive formula of a GP is
\(a_n=6a_{n-1}\)
It is given that the first term is 0.75, it means
\(a_1=0.75\)
The next terms of GP are
\(a_2=6a_{2-1}=6\times (0.75)=4.5\)
\(a_3=6a_{3-1}=6\times (4.5)=27\)
The GP is defined as
\(0.75,4.5,27\)
Here the first term is 0.75 and the common ratio is 6.
The explicit formula for the nth term of a GP is
\(a_n=ar^{n-1}\)
The explicit formula for the nth term of the sequence
\(a_n=0.75(6)^{n-1}\)
Therefore the explicit formula for the nth term of the sequence is \(a_n=0.75(6)^{n-1}\).
