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`?
0.81 = 0.8
0.82 = 0.64
0.83 = 0.512
0.84 = 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: 1.23 = 1.728
Answer: 1.2