Question

Write an equation to describe the sequence below use and to represent the position of a term in the sequence where n equals one for the first term 1, 4, 16

Answer 1

an = 4^(n-1)

Explanation:

The three given terms have a common ratio of 4:

4/1 = 16/4 = 4

So, this can be described by the function for a geometric sequence:

an = a1×r^(n -1)

where an is the n-th term, a1 is the first term (1) and r is the common ratio (4).

an = 1×4^(n-1)

an = 4^(n -1) . . . . . simplified