Question

How do you find `a_6` for the geometric sequence `540, 90, 15,...`?

Answer 1

The sixth term `a_6` is `5/72`

Explanation:

In a geometric series, whose first term is `a_1` and common ratio is `r`, `n^(th)` term `a_n` is given by `a_1xxr^(n-1)`.

In the given series `{540,90,15,....}`, first term is `540` and common ration `r` is `90/540=15/90=1/6`

Hence the sixth term `a_6` is `a_1xxr^(n-1)=540xx1/6^(6-1)`

= `540/(6xx6xx6xx6xx6)=(6xx6xx3xx5)/(6xx6xx6xx6xx6)`

= `(cancel6xxcancel6xxcancel3xx5)/(cancel6xxcancel6xx2cancel6xx6xx6)`

= `5/72`