The fourth term of a sequence is 108. Each term after the first is 3 times the previous term. Write an explicit expression that models the general term of the sequence f(n). Write your answer in the space provided on your answer document.
Accepted Solution
A:
Answer:[tex]f(n)=4(3)^{n-1}[/tex]Step-by-step explanation:Let the first term be [tex]x[/tex], then the terms of the sequence are:[tex]x,3x,9x,27x,81x,...[/tex].Since the fourth term is 108, we have [tex]27x=108[/tex][tex]\implies x=4[/tex]Hence the sequence becomes:[tex]4,12,36,108,324,...[/tex].The explicit expression for a geometric expression is given by:[tex]f(n)=ar^{n-1}[/tex]where a=4 and r=3The required formula is:[tex]f(n)=4(3)^{n-1}[/tex]