Question

find the 8th term of geometric sequence where a1=5, r= -2

Answer 1

for Given:

$\begin{gathered} a_1=5 \\ r=-2​ \end{gathered}$

You need to remember that "r" is the Common ratio between the terms of the Geometric Sequence and this is the first term:

$a_1_{}_{}$

The formula the nth term of a Geometric Sequence is:

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

Where "n" is the number of the term, "r" is the Common Ratio, and the first term of the sequence is:

$a_1$

In this case, since you need to find the 8th term, you know that:

$n=8$

Then, you can substitute all the values into the formula:

$a_8=(5)(-2)^{(8-1)}$

Evaluating, you get:

$\begin{gathered} a_8=(5)(-2)^{(7)} \\ a_8=(5)(-128) \\ a_8=-640 \end{gathered}$

Hence, the answer is:

$a_8=-640$