Question

What is the eighth term of the geometric sequence 4,-20,100,...?

Answer 1

Well, let's see the sequence, 4, -20, 100.....

so... is a geometric sequence, that means, you get to the next value by multiplying the current one by "something", that something is the "common ratio", what can it be?

well, since let's say is "r", so, since we multiplied 4 times "r" to get -20, then -20/4 = r no?

that is, 4 * r = -20
                4 = -20/4

anyway, so, we get -5 as the "common ratio", and the first number is 4, now, we're looking for the 8th term's value.

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=4\\ r=-5\\ n=8 \end{cases}\implies a_8=4(-5)^{8-1}$

Answer 2

76,196,172,292,268 THE ANSWER IS 268