Question

Find the 13th term of the geometric sequence 7, -35, 175, ...Even after reviewing a few time I really don't understand how to do these

Answer 1

Given

$7,-35,175$

Recall

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

Where

$\begin{gathered} a_n=nth\text{ term} \\ a_1=first\text{ term} \\ r=comon\text{ ratio} \\ n=term\text{ position} \end{gathered}$

Now

$r=\frac{a_2}{a_1}=-\frac{35}{7}=-5$

Therefore,

$\begin{gathered} a_{13}=7(-5)^{13-1} \\ a_{13}=7(-5)^{12} \\ \\ a_{13}=7(244140625) \end{gathered}$

The final answer

1708984375