Question 1188018
<br>
S(n) = a+ar+ar^2+...+ar^(n-1)<br>
S(n) = a(1+r+r^2+...+r^(n-1)<br>
{{{S(n) = a((1-r^n)/(1-r))}}}<br>
We are given a=3/8, r=-2, and S(n) = -8191.875.  Plug the numbers into the formula to determine n.<br>
{{{-8191.875 = (3/8)((1-(-2)^n)/(1-(-2))) = (3/8)((1-(-2)^n)/3) = (1/8)((1-(-2)^n))}}}
{{{1-(-2)^n = 8(-8191.875)=-65535}}}
{{{-(-2)^n = -65536 = -2^16}}}
{{{n=16}}}<br>
We are to find the sum of the (n+1) term to the (n+5) term, or the sum of the 17th to 21st terms, which is S(21)-S(16).<br>
{{{S(21) = (1/8)((1-(-2)^21)) = 262144.125}}}<br>
And then<br>
{{{S(21)-S(16) = 262144.125-(-8191.875) = 270336}}}<br>
ANSWER: 270336<br>