Geometric Progressions

Geometric Progressions

GCSE(F), GCSE(H),

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.

Examples

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

Answer: 0.8, 0.64, 0.512, 0.4096

0.81 = 0.8

0.82 = 0.64

0.83 = 0.512

0.84 = 0.4096

2. 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 ?

Answer: 1.2

`1.44 = r^2`, therefore `r = √1.44 = 1.2`

`r^1 = 1.2`

Check with a subsequence term: 1.23 = 1.728