Hi Glen,

You know that the common ration r is 2.5 since 0.1024 × 2.5 = 0.256. Thus you know the third term is

0.256 × 2.5 = 0.1024 × 2.5² = 0.64

and the fourth term is

0.64 × 2.5 = 0.1025 × 2.5³

etc.

What I hope you see here is that each term is 0.1025 × 2.5^power where power is one less than the term number. So, for example the fifth term is 0.1025 × 2.5^5-1 = 0.1025 × 2.5⁴.

Thus if the middle term is term number m then the middle term is 0.1025 × 2.5^m-1. Hence

0.1025 × 2.5^m-1 = 156.25

so

2.5^m-1 = 156.25/0.1025.

Evaluate the right side and then use logarithms to solve for m.

I hope this helps,
Penny