Question

What is the 6th term of this geometric sequence 3, –9, 27, –81, …?

Answer 1

`color(blue)(-729`

Explanation:

the geometric sequence given is:
`3 , -9 , 27 , -81` ...

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 the common ratio `r = -3` the first term `a = 3`
and `n = 6`

The 6th term can be obtained through formula
`T_n = ar^(n-1) = 3 xx -3^((6-1))`
`= 3xx -3^5`
`= 3 xx -243= color(blue)(-729`