Question

What is the sum of the first five terms of the geometric sequence in which a1=5 and r=1/5

Answer 1

Answer:

Sum of the first five terms of the geometric sequence in which a1=5 and r=1/5 is $\mathbf{S_n=\frac{781}{125} }$

Step-by-step explanation:

We need to find sum of the first five terms of the geometric sequence in which a1=5 and r=1/5

The formula used to find sum of the geometric sequence is: $S_n=\frac{a(r^n-1)}{r-1}$

Where a is the first term, r is the common ratio and n is the number of terms

Now finding sum of the first five terms of the geometric sequence

We have a=5, r=1/5 and n=5

Putting values in the formula:

$S_n=\frac{a(r^n-1)}{r-1}\\S_n=\frac{5((\frac{1}{5}) ^5-1)}{\frac{1}{5}-1}\\S_n=\frac{5(\frac{1}{3125}-1)}{\frac{1-5}{5}}\\S_n=\frac{5(\frac{1-3125}{3125})}{\frac{-4}{5}}\\S_n=\frac{5(\frac{-3124}{3125})}{\frac{-4}{5}}\\S_n=5(\frac{-3124}{3125})}\times{\frac{-5}{4}}\\S_n=\frac{781}{125}$

So, sum of the first five terms of the geometric sequence in which a1=5 and r=1/5 is $\mathbf{S_n=\frac{781}{125} }$