Question

Find the sum of the first 7 terms of the following sequence. Round to the nearest hundredth if necessary.5,−2,45,...5,−2, 54 ,...Sum of a finite geometric series:Sum of a finite geometric series:Sn=a1−a1rn1−rS n = 1−ra 1 −a 1 r n

Answer 1

Given:

`5,-2,(4)/(5),\ldots`

To get the sum of the first 7 terms, the formula below is used;

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

where;

`\begin{gathered} n=7 \\ a_1\text{ is the first term = 5} \\ r\text{ is the co}mmon\text{ ratio=}(-2)/(5) \end{gathered}`

Hence,

`\begin{gathered} S_n=(a_1-a_1r^n)/(1-r) \\ S_7=(5-5(-(2)/(5))^7)/(1-(-(2)/(5))) \\ S_7=(5-5(-0.4)^7)/(1+(2)/(5)) \\ S_7=(5-5(-0.0016384))/(1+0.4) \\ S_7=(5+0.008192)/(1.4) \\ S_7=(5.008192)/(1.4) \\ S_7=3.57728 \end{gathered}`

Therefore, the sum of the first 7 terms is 3.57728