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.
Explanation:
The given sequence is:
7,21,63, …
The first term a = 7
Common ratio r=
[tex]\begin{gathered} \frac{21}{7}=3 \\ \frac{63}{21}=3 \end{gathered}[/tex]The given sequence is a geometric series.
The sum of n terms of the geometric series is given by the formula:
[tex]a_n=\frac{a(r^n-1)}{r-1}[/tex]The sum of the first 8 terms:
[tex]\begin{gathered} a_8=\frac{7(3^8-1)}{3-1} \\ a_8=\frac{7(6561-1)}{2} \\ a_8=\frac{7(6560)}{2} \\ a_8=7\times3280 \\ a_8=22,960 \end{gathered}[/tex]Final Answer:
The sum of the first 8 terms of the given sequence is 22,960.
