Question

How do you find the explicit formula for the following sequence 3, 6, 12, 24, 48, . . .?

Answer 1

`n^(th)` term of the geometric sequence is given by `3*2^(n-1)`

Explanation:

`3, 6, 12, 24, 48, . . .` is a geometric sequence with `3` as first term and subsequent terms being multiplied by `2`. In a geometric sequence with `a` as first term and subsequent terms being multiplied by `r`, `n^(th)` term is given by

`a*r^(n-1)` and hence `n^(th)` term of the geometric sequence is given by

`3*2^(n-1)`