Answer:
\(\frac{1562}{125}\)
Step-by-step explanation:
We are given that
\(a_1=a=10, r=\frac{1}{5}=0.2\)
We have to find the sum of first five terms of geometric series.
We know that nth term in geometric series is given by
\(a_n=ar^{n-1}\)
\(a_2=10(\frac{1}{5})=2\)
\(a_3=10(\frac{1}{5})^2=\frac{2}{5}\)
\(a_4=ar^3=10(\frac{1}{5})^3=\frac{2}{25}\)
\(a_5=ar^4=10(\frac{1}{5})^4=\frac{2}{125}\)
\(S_5=a_1+a_2+a_3+a_4+a_5\)
Substitute the values then, we get
\(S_5=10+2+\frac{2}{5}+\frac{2}{25}+\frac{2}{125}=\frac{1250+250+50+10+2}{125}=\frac{1562}{125}\)
Hence, the sum of first five terms in geometric series =\(\frac{1562}{125}\)
