Question

What is the sum of the first five terms of a geometric series with a1 = 20 and r = 1/4?

Express your answer as an improper fraction in lowest terms without using spaces.

Answer 1

For the answer to the question above,
The first term is 20 
The second term is 20* 1/4 = 5 
The third term is 5 * 1/4 = 5/4 
The 4th term is 5/4 * 1/4 = 5/16 
The 5th term is 5/16 * 1/4 = 5/64 

Sum is therefore 20 + 5 + 5/4 + 5/16 + 5/64 
To complete my answer,
= (1280 + 320 + 80 + 20 + 5) / 64 
= 1705/64

I hope my answer helped you. Have a nice day!

Answer 2

The sum of the first five terms is 1705/64

How to find geometric sum

Using the formula

The sum of a GP when r ∠ 1 , SN = s1 + s2 + s3 + s4 + s5

r =  1/4

a = 20

n = 5

S1 = 20

S2 = 20* 1/4 = 5

S3=5 * 1/4 = 5/4

S4 = 5/4 * 1/4= 5/16

S5 = 5/16* 1/4 = 5/64

The sum of the terms = 5 + 5+ 5/4+ 5/16 + 5/64 = 1705/64

Thus, the sum of the first five terms is 1705/64

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