What is the sum of the geometric sequence -3, 18, -108, … if there are 7 terms?

3 Answers
Jim G.
Aug 14, 2018

#S_7=-119973#

Explanation:

#"the sum to n terms for a geometric sequence is"#

#•color(white)(x)S_n=(a(r^(n-1)))/(r-1)#

#"where a is the first term and r the common ratio"#

#a=-3" and "r=(-108)/18=18/(-3)=-6#

#S_7=(-3((-6)^7-1))/(-6-1)#

#color(white)(xx)=(-3(-279936-1))/(-7)#

#color(white)(xx)=(-3xx-279937)/(-7)=-19973#

maganbhai P.
Aug 14, 2018

#S_7=-119973#

Explanation:

Here,

#-3,18,-108,..."are in GP"#

Let ,first term #=a_1=-3 and #

common ratio #=r=(-108)/18=18/(-3)=-6#

So, the sum of first n terms is:

#S_n=(a_1(1-r^n))/(1-r) ,where, n=7#

#:S_7=(-3(1-(-6)^7))/(1-(-6))#

#:.S_7=-(3(1+279936))/7=-(3(279937))/7=-119973#

Jake M.
Aug 14, 2018

-119973

Explanation:

We can first see that the ratio between these is #-6#. This means we have the sum of a geometric series, which we know is
#S_n = a_1 * (r^n-1)/(r-1) = -3 * ((-6)^7 - 1)/((-6)-1) = -119973#

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