Question

Find the exact value of the eighth term of the geometric sequence: 648, 216, 72, 24,

Answer 1

8/27

Step-by-step explanation:

First, determine the common ratio of the geometric sequence:

`\begin{gathered} (216)/(648)=(1)/(3) \\ (72)/(216)=(1)/(3) \\ \implies r=(1)/(3) \end{gathered}`

The nth term of any geometric sequence is obtained using the formula:

`\begin{gathered} T_n=ar^(n-1) \\ a=\text{first term} \end{gathered}`

Thus, the 8th term will be:

`\begin{gathered} T_8=648*\mleft((1)/(3)\mright)^(8-1) \\ _{}=648*(1^7)/(3^7) \\ =\frac{648}{2187^{}} \\ T_8=(8)/(27) \end{gathered}`

The exact value of the eighth term of the geometric sequence is 8/27.