Question

Geometric sequence help pls

Answer 1

-1220703125 is the 14th term of the geometric sequence.

Explanation:

The following geometric sequence has the common ratio of -5 as -5/1 = -5 and 25/-5 = -5.

Then apply in the geometric sequence formula which is:

`\displaystyle{a_n = a_1r^(n-1)}`

where
`a_n` represents the nth term,
`a_1` is the 1st term and
`r` is the common ratio. Substitute in the known values:

`\displaystyle{a_n = 1\left(-5\right)^(n-1)}\\\\\displaystyle{a_n = \left(-5\right)^(n-1)}`

Since we want to find the 14th term of the sequence, substitute n = 14:

`\displaystyle{a_(14)=\left(-5\right)^(14-1)}\\\\\displaystyle{a_(14)=\left(-5\right)^(13)}\\\\\displaystyle{a_(14)=-1220703125}`