A geometric sequence is based on raising a number to a power, where the power is the term.

This is written as `u_n = ar^n`, where `u_n` is the value for the term, *a* is a constant, and `r^n` is a number raised to the term.

What are the values for the first four terms in the sequence given by `u_n = 0.8^n`?

0.8^{1} = 0.8

0.8^{2} = 0.64

0.8^{3} = 0.512

0.8^{4} = 0.4096

Answer: 0.8, 0.64, 0.512, 0.4096

In a sequence `u_n = r^n`, What is the value of the first term in this sequence:

..., 1.44, 1.728, 2.0736, 2.48832 ?

`u_2 = r^2`

`1.44 = r^2`

`r = 1.2`

Check with a subsequence term: 1.2^{3} = 1.728

Answer: 1.2

Check out our iOS app: tons of questions to help you practice for your GCSE maths. Download free on the App Store (in-app purchases required).