Question

What is S5 for 1000 + 500 + 250 + ... ?

Answer 1

1000 + 500 + 250 + 125 + 62.5 = 1,937.5

Answer 2

The sum of first five term is 1937.5.

Explanation:

The given series is

`1000+500+250+...`

Here the first term is 1000 and each term is half of its previous term. The common ratio is

`r=(500)/(1000)=0.5`

The sum of n terms of a GP is

`S_n=(a(1-r^n))/(1-r)`

Where, a is first term, r is common difference, r<1 and n is number of terms.

`S_5=(1000(1-(0.5)^5))/(1-0.5)`

`S_5=(968.75)/(0.5)`

`S_5=1937.5`

Therefore the sum of first five term is 1937.5.