Given:
The geometric sequence
[tex]12,18,27..............[/tex]Find-:
The sum of the first 8 terms of the geometric sequence
Explanation-:
The sum of a geometric sequence is:
Where,
[tex]\begin{gathered} a=\text{ First terms} \\ \\ r=\text{ Common ratio} \\ \\ n=\text{ Number of term} \\ \\ S_n=\text{ Sum of the first n terms } \end{gathered}[/tex]The geometric sequence is:
[tex]12,18,27...........[/tex][tex]\text{ First terms }(a)=12[/tex]The common ratio is:
[tex]\begin{gathered} r=\frac{a_n}{a_{n-1}} \\ \\ r=\frac{18}{12} \\ \\ r(\text{ common ratio\rparen}=1.5 \end{gathered}[/tex]Sum of the first 8 terms is:
[tex]n=8[/tex]So, the sum of the first 8 terms is:
r is greater than 1, so the formula is:
[tex]\begin{gathered} S_n=\frac{a(r^n-1)}{r-1} \\ \\ S_8=\frac{12((1.5)^8-1)}{1.5-1} \\ \\ S_8=\frac{12(25.63-1)}{1.5-1} \\ \\ S_8=\frac{12(24.63)}{0.5} \\ \\ S_8=\frac{295.55}{0.5} \\ \\ S_8=591.09 \end{gathered}[/tex]The sum of the first 8 terms is 591.09
