Question

For a given geometric sequence, the 9th term, ag. is equal to -43/64and the 13th term, Q13, is equal to - 172. Find the value of the 17th term, a17. If applicable,write your answer as a fraction.

Answer 1

Answer:

The value of the 17th term is;

$a_{17}=-44032$

Explanation:

Given that;

For a given geometric sequence, the 9th term is equal to

$a_9=-\frac{43}{64}$

the 13th term, Q13, is equal to - 172.

$a_{13}=-172$

Recall that for geometric progression;

$\frac{a_{13}}{a_9}=r^4$

where r is the common ratio

substituting the given;

$\begin{gathered} r^4=\frac{a_{13}}{a_9}=\frac{-172}{(-\frac{43}{64})} \\ r^4=\frac{-172}{(-\frac{43}{64})}=172\times\frac{64}{43} \\ r^4=4\times64 \\ r^4=256 \\ r=\sqrt[4]{256} \\ r=4 \end{gathered}$

To find the value of the 17th term;

$\begin{gathered} a_{17}=a_{13}\times r^4 \\ a_{17}=-172\times4^4 \\ a_{17}=-44032 \end{gathered}$

Therefore, the value of the 17th term is;

$a_{17}=-44032$