Question

What is the 8th term of the geometric sequence 3, 9, 27,...?

Answer 1

The geometric sequence given is:
`3 , 9 , 27` ...

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) `9/3 = 3`
2) `27/9= 3`

for this sequence:

• common ratio `r = 3`
• first term `a = 3`
• `n = 8`

The 8th term can be obtained through formula
`T_n = ar^(n-1) = 3 xx 3^((8-1))`
`= 3 xx 3^7`
`= 3 xx 2187= 6561`