37.8k views
1 vote
Find the sum of the first 8 terms of the geometric sequence that begins: 12, 18, 27, ...

Can you provide a detail explanation to find sum of first 8 terms?Thanks.

User Pscl
by
8.3k points

1 Answer

4 votes

Given:

The geometric sequence


12,18,27..............

Find-:

The sum of the first 8 terms of the geometric sequence

Explanation-:

The sum of a geometric sequence is:

Where,


\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}

The geometric sequence is:


12,18,27...........
\text{ First terms }(a)=12

The common ratio is:


\begin{gathered} r=(a_n)/(a_(n-1)) \\ \\ r=(18)/(12) \\ \\ r(\text{ common ratio\rparen}=1.5 \end{gathered}

Sum of the first 8 terms is:


n=8

So, the sum of the first 8 terms is:

r is greater than 1, so the formula is:


\begin{gathered} S_n=(a(r^n-1))/(r-1) \\ \\ S_8=(12((1.5)^8-1))/(1.5-1) \\ \\ S_8=(12(25.63-1))/(1.5-1) \\ \\ S_8=(12(24.63))/(0.5) \\ \\ S_8=(295.55)/(0.5) \\ \\ S_8=591.09 \end{gathered}

The sum of the first 8 terms is 591.09

Find the sum of the first 8 terms of the geometric sequence that begins: 12, 18, 27, ... Can-example-1
User Zlatko
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories