Question

Find the ninth term of the geometric sequence a4= -135,r=-3

Answer 1

The nth term of the geometric sequence is is 32805

Explanation:

The nth term of a geometric sequence is given by

`$ a_n = a_1 \cdot r^(n - 1) $`

Where
`a_1\\` is the first term and
`r` is the common ratio

We are given the fourth term of this sequence

`a_4 = -135`

The common ratio is

`r = -3`

Once we find the 1st term then we can find any other term.

`a_4 = a_1 \cdot r^(4 - 1) \\\\a_4 = a_1 \cdot r^(3) \\\\-135 = a_1 \cdot (-3)^(3) \\\\-135 = a_1 \cdot (-27) \\\\a_1 = (-135)/(-27) \\\\a_1 = 5`

So the ninth term of this geometric sequence is

`a_n = a_1 \cdot r^(n - 1) \\\\a_9 = a_1 \cdot r^(9 - 1) \\\\a_9 = a_1 \cdot r^(8) \\\\a_9 = 5 \cdot (-3)^(8) \\\\a_9 = 5 \cdot (6561) \\\\a_9 = 32805`

Therefore, the nth term of the geometric sequence is is 32805