Question

2, 4, 8, 16. Write the recursive and explicit functions for each geometric sequence.

Answer 1

Given

{2, 4, 8, 16, ...}

Procedure

A recursive formula allows us to find any term of a geometric sequence by using the previous term.

$a_n=2\cdot a_{n-1}$

Because a geometric sequence is an exponential function whose domain is the set of positive integers, and the common ratio is the base of the function, we can write explicit formulas that allow us to find particular terms.

$a_n=2^n$