Question

What is the 7th term of the geometric sequence 4, 20, 100,...?

Answer 1

The geometric sequence given is:
`4 , 20 , 100` ...

When provided with a geometric sequence we must first calculate the common ratio `r`

`r` is obtained by dividing a term by its preceding term
1) `20/4 = 5`
2) `100/20 = 5`

for this sequence the common ratio `r = 5` the first term `a = 4`
and `n = 7`

The 7th term can be obtained through formula
`T_n = ar^(n-1) = 4 xx 5^((7-1))`
`= 4 xx 5^6`
`= 4 xx 15625= 62500`