Answer:
Option 4
Step-by-step explanation:
Given : Geometric sequence [tex]a_n=20\times (\frac{1}{2})^{n-1}[/tex]
To find : Which spreadsheet would be used to compute the first 7 terms of the geometric sequence ?
Solution :
Geometric sequence is in the form [tex]a+ar+ar^2+ar^3+...[/tex]
Where, a is the first term and r is the common ratio.
The sum of sequence is represented as [tex]S_n=\sum^{7}_{n=0} ar^n[/tex]
or [tex]S_n=\sum^{7}_{n=1} ar^{n-1}[/tex]
According to question,
a=20 and [tex]r=\frac{1}{2}[/tex]
Sum of first terms is,
[tex]S_1=20(\frac{1}{2})^{n_1-1}[/tex] , [tex]n_1=1[/tex]
Sum of second terms is,
[tex]S_2=20(\frac{1}{2})^{n_2-1}[/tex] ,[tex]n_2=2[/tex]
Sum of third terms is,
[tex]S_3=20(\frac{1}{2})^{n_3-1}[/tex] ,[tex]n_3=3[/tex]
Sum of four terms is,
[tex]S_4=20(\frac{1}{2})^{n_4-1}[/tex] ,[tex]n_4=4[/tex]
Sum of five terms is,
[tex]S_5=20(\frac{1}{2})^{n_5-1}[/tex] ,[tex]n_5=5[/tex]
Sum of six terms is,
[tex]S_6=20(\frac{1}{2})^{n_6-1}[/tex] ,[tex]n_6=6[/tex]
Sum of seven terms is,
[tex]S_7=20(\frac{1}{2})^{n_7-1}[/tex] ,[tex]n_7=7[/tex]
Therefore, Option 4 is correct.
The spreadsheet 4 would be used to compute the first 7 terms of the geometric sequence.
