We are given the following sequence
[tex]-3,15,-75,375,\ldots[/tex]Let us find a general formula for this sequence.
Recall that the geometric sequence is given by
[tex]a_n=a_1r^{n-1}[/tex]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
[tex]\begin{gathered} r=\frac{375}{-75}=-5 \\ r=\frac{-75}{15}=-5 \\ r=\frac{15}{-3}=-5 \end{gathered}[/tex]So, the common ratio is -5
The first term of the sequence is -3
So, the general formula for the given sequence becomes
[tex]a_n=-3(-5)^{n-1}[/tex]Now, let us find the 8th term of this sequence
Substitute n = 8 into the above formula
[tex]a_8=-3(-5)^{8-1}=-3(-5)^7=-3(-78125)=234375[/tex]Therefore, the 8th term of the sequence is 234375
