Question

What is the 6th 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 = 6`

The 6th term can be obtained through formula
`T_n = ar^(n-1) = 4 xx 5^((6-1))`
`= 4 xx 5^5`
`= 4 xx 3125 = 12500`