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`