Question

Determine whether the sequence below is arithmetic or geometric, and find the function that will produce any given term in the sequence: 16, 24, 36, 54, 81,

Is this sequence arithmetic?
Is this sequence Geometric?
What is the analytical representation of the sequence?

Answer 1

Geometric Sequence.

nth term = an = 16(1.5^(n-1).

Explanation:

24/16 = 1.5

36/24 = 1.5

54/36 = 1.5

81/54 = 1.5

There is a common ratio between the terms so it is Geometric.

The nth term an = a1r^(n-1) where a1 = first term , r = common ratio.

So here we have an = 16(1.5)^(n-1).