Question

How do you find the 4th, 5th, 6th, and 7th term of the geometric sequence 7, 21, 63...?

Answer 1

The general term of a geometric sequence of common ratio `r` and first term `a` is given by
`T_n=ar^(n-1)`

In this case the first term is `a=7` and since it is a geometric sequence, it has a common ratio
`r=21/7=63/21=3`.

Hence general term `T_n=7*(3)^(n-1)`.

`therefore T_4=7*3^(4-1)=189`

`T_5=7*3^(5-1)=567`

Similarly `T_6=1701 and T_7=5103`