Question

Find the sum of the first 7 terms of the following sequence. Round to the nearesthundredth if necessary.

Answer 1

Given the sequence:

`50,61,74.42,\ldots`

The given sequence has a common ratio = r

`r=(61)/(50)=(74.42)/(61)=1.22`

we will find the sum of the first 7 terms as follows:

`\begin{gathered} S_n=(a_1-a_1\cdot r^n)/(1-r) \\ \\ a_1=50 \\ r=1.22 \\ n=7 \end{gathered}`

Substitute with a1, r, and n into the formula Sn

so,

`S_7=(50-50\cdot(1.22)^7)/(1-1.22)=686.9797`

Round to the nearest hundredth

So, the answer will be sum = 686.98