What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms?

1 Answer
Nov 26, 2015

-87378.66bar687378.66¯6

Explanation:

The sum of an nn term geometric sequence with initial term a_0a0 and ratio rr (i.e. a_i=a_(i-1)*rai=ai1r)
is given by the equation:
color(white)("XXX")sum_(i=0)^(n-1)a_i = (a_0*(1+r)^n)/(1-r)XXXn1i=0ai=a0(1+r)n1r

In this case a_0 = 8a0=8 and r=(-2)r=(2)

So the sum is
color(white)("XXX")=(8*(1+(-2)^15))/(1-(-2))XXX=8(1+(2)15)1(2)

color(white)("XXX")=(8*(1+(-32768)))/3XXX=8(1+(32768))3

color(white)("XXX")=(8*(-32767))/3XXX=8(32767)3

color(white)("XXX")=(-262136)/3XXX=2621363

color(white)("XXX")=-(87378 2/3)XXX=(8737823)