Question

How do you write the expression for the nth term of the geometric sequence `a_1=1000, r=1.005, n=60`?

Answer 1

`a_n=1000xx1.005^n` and for `n=60`, `a_60=1348.85`

Explanation:

In a geometric sequence, where first term is `a_1` and common ratio is `r`,

`n^(th)` term `a_n` is given by `a_1xxr^(n-1)`

Hence `n^(th)` term of a geometric sequence whose first term is `a_1=1000` and common ratio is `r=1.005` is

`a_n=1000xx1.005^n`

and `a_60=1000xx1.005^60~=1000xx1.34885=1348.85`,

where value of `1.005^60` has been approximated up to `5dp`.