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

1 Answer
Alan P.
Nov 26, 2015

#-87378.66bar6#

Explanation:

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

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

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

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

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

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

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

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