Answer:
The first term is 81
Step-by-step explanation:
The common ratio is 2/3.
[tex]r = \frac{2}{3} <1[/tex]
Sum of first n terms in GP = [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
The sum of the first 3 terms of a geometric series is 171
n=3
Substitute the values in the formula:
[tex]S_3=\frac{a(1-(\frac{2}{3})^3}{1-\frac{2}{3}}[/tex]
[tex]171=\frac{a(1-(\frac{2}{3})^3)}{1-\frac{2}{3}}[/tex]
[tex]171(1-\frac{2}{3})=a(1-(\frac{2}{3})^3)[/tex]
[tex]\frac{171(1-\frac{2}{3})}{(1-(\frac{2}{3})^3)}=a[/tex]
[tex]81=a[/tex]
Hence The first term is 81
