Answer:
The sum of first five term is 1937.5.
Step-by-step explanation:
The given series is
[tex]1000+500+250+...[/tex]
Here the first term is 1000 and each term is half of its previous term. The common ratio is
[tex]r=\frac{500}{1000}=0.5[/tex]
The sum of n terms of a GP is
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
Where, a is first term, r is common difference, r<1 and n is number of terms.
[tex]S_5=\frac{1000(1-(0.5)^5)}{1-0.5}[/tex]
[tex]S_5=\frac{968.75}{0.5}[/tex]
[tex]S_5=1937.5[/tex]
Therefore the sum of first five term is 1937.5.
