Question

Find the sum of the first 8 terms of the following sequence 7,21,63, …Round to the nearest hundredth if necessary.

Answer 1

Given:

The sequence is: 7,21,63, …

Required:

Find the sum of the first 8 terms of the given sequence. Round to the nearest hundredth if necessary.

Step-by-step explanation:

The given sequence is:

7,21,63, …

The first term a = 7

Common ratio r=

`\begin{gathered} (21)/(7)=3 \\ (63)/(21)=3 \end{gathered}`

The given sequence is a geometric series.

The sum of n terms of the geometric series is given by the formula:

`a_n=(a(r^n-1))/(r-1)`

The sum of the first 8 terms:

`\begin{gathered} a_8=(7(3^8-1))/(3-1) \\ a_8=(7(6561-1))/(2) \\ a_8=(7(6560))/(2) \\ a_8=7*3280 \\ a_8=22,960 \end{gathered}`

Final Answer:

The sum of the first 8 terms of the given sequence is 22,960.