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DochEvi [55]
2 years ago
5

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

Mathematics
1 answer:
den301095 [7]2 years ago
3 0

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} }

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