Question

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.

Answer 1

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