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2 years ago

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

Mathematics

2 answers:

leva [86]2 years ago

3 0

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

Bas_tet [7]2 years ago

3 0

Answer:

The sum of first five term is 1937.5.

Step-by-step 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

$r=\frac{500}{1000}=0.5$

The sum of n terms of a GP is

$S_n=\frac{a(1-r^n)}{1-r}$

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

$S_5=\frac{1000(1-(0.5)^5)}{1-0.5}$

$S_5=\frac{968.75}{0.5}$

$S_5=1937.5$

Therefore the sum of first five term is 1937.5.

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