Problema Solution

the first term of the geometric series is -1,and the common ratio is -3. how many terms are in the series is its sum is 182?

Answer provided by our tutors

1st term = -1 and common ratio = -3

let there are n terms in the series

then the total sum is given by

 

a*(r^n-1)/(r-1) = (-1)((-3)^n - 1)/(-3-1) =182

 

==> (-3)^n - 1 = 182*4 = 728

==> (-3)^n = 729 = 3^6 = (-3)^6

==> n=6

Hence, there are total 6 terms in the series.