Question

A geometric sequence starts with 10, 5, . . . Explain how you would calculate the value of the 100th term.

Answer 1

The 100th term will be;

10(0.5)^99

Explanation:

Firstly, we need the common difference and the first term

The first term is 10

The common difference is 5/10 = 1/2

Now, the formula for the nth term of a geometric sequence is;

ar^n-1

So, for the nth term, we have;

ar^(100-1)

= ar^99

So we have

10(1/2)^99