Question

For the sequence -3, 15 -75, 375,… what is the 8th term?234 375-234 37532-32

Answer 1

We are given the following sequence

`-3,15,-75,375,\ldots`

Let us find a general formula for this sequence.

Recall that the geometric sequence is given by

`a_n=a_1r^(n-1)`

Where aₙ is the nth term, a₁ is the first term and r is the common ratio

The common ratio is basically the ratio between any two consecutive terms

`\begin{gathered} r=(375)/(-75)=-5 \\ r=(-75)/(15)=-5 \\ r=(15)/(-3)=-5 \end{gathered}`

So, the common ratio is -5

The first term of the sequence is -3

So, the general formula for the given sequence becomes

`a_n=-3(-5)^(n-1)`

Now, let us find the 8th term of this sequence

Substitute n = 8 into the above formula

`a_8=-3(-5)^(8-1)=-3(-5)^7=-3(-78125)=234375`

Therefore, the 8th term of the sequence is 234375