Answer :
Answer:
S6 = 22
Explanation:
Given the series:
[tex]15,5,\frac{5}{3}\cdots[/tex]The sequence is a geometric sequence with:
• The first term, a = 15
,• The common ratio, r = 1/3
The sum of nth terms of a geometric sequence is determined using the formula:
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]Substitute a=15, r=1/3 and n=6.
[tex]\begin{gathered} S_6=\frac{15(1-(\frac{1}{3})^6)}{1-\frac{1}{3}} \\ =\frac{15(1-\frac{1}{729})}{\frac{2}{3}} \\ =\frac{15(\frac{728}{729})}{\frac{2}{3}} \\ =\frac{1820}{81} \\ =22.47 \\ \implies S_6\approx22 \end{gathered}[/tex]The sum of the first 6 ters of the series is 22. (roundd to the nearest integer)