Question

Show that the sequence given by `T_(n)=(2xx3^(n))` for all `n in N` is a GP. Find its first term and the common ratio.

Answer 1

We have
`T_(n)=(2xx3^(n))` and `T_(n+1)=(2xx3^(n+1))`.
`:. T_(n+1)/T_(n)=(2xx3^(n+1))/(2xx3^(n))=3` (constant) for all `n in N`.
Also, `T_(1)=(2xx3^(1))=(2xx3)=6`
`:.` the first term `=6` and the common ratio `=3`.