Question

Find the sum of the first 6 terms of the following sequence. Round to the nearest

hundredth if necessary.
324,
54,
9….

Answer 1

• a=324 [A1 to be used as a]
• Common ratio:=r=9/54=1/6

So

`\\ \rm\Rrightarrow S_n=(a-ar^n)/(1-r)`

`\\ \rm\Rrightarrow S_6=(324-324(1/6)^6)/(1-1/6)`

`\\ \rm\Rrightarrow S_6=(324-(1)/(12^2))/((5)/(6))`

`\\ \rm\Rrightarrow S_6=(9331)/(24)=388.79`

Answer 2

388.79 (nearest hundredth)

Explanation:

Given sequence: 324, 54, 9, ...

Therefore:

`a_1=324`

`r=\textsf{common ratio}=(54)/(324)=\frac16`

Sum of a finite geometric series:

`S_n=(a_1-a_1r^n)/(1-r)`

Sum of the first 6 terms → n= 6:

`\begin{aligned}S_6 & =(324-324(\frac16)^6)/(1-\frac16)\\ & =(324-(1)/(144))/(1-\frac16)\\ & =(9331)/(24)\\ & = 388.79\:\textsf{(nearest hundredth)}\end{aligned}`