Question

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

Answer 1

`-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)`