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

The value of the 17th term is;

`a_(17)=-44032`

Step-by-step explanation:

Given that;

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

`a_9=-(43)/(64)`

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

`a_(13)=-172`

Recall that for geometric progression;

`(a_(13))/(a_9)=r^4`

where r is the common ratio

substituting the given;

`\begin{gathered} r^4=(a_(13))/(a_9)=(-172)/((-(43)/(64))) \\ r^4=(-172)/((-(43)/(64)))=172*(64)/(43) \\ r^4=4*64 \\ 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)* r^4 \\ a_(17)=-172*4^4 \\ a_(17)=-44032 \end{gathered}`

Therefore, the value of the 17th term is;

`a_(17)=-44032`