How do you find the sum of the geometric series #2-10+50-...# to 6 terms?

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Answer 1 · 2016-11-25T22:30:14

#S_n=-5208#

Find the sum of the geometric sequence #2, -10, 50...# to 6 terms.

A geometric sequence is formed by multiplying a term by a number called the common ratio #r# to get the next term.

The formula for a sum of a geometric sequence is

#S_n=frac(a_1(1-r^n))(1-r)#
where #a_1# is the first term, #r# is the common ratio, and #n# is the number of the term,

In this example, #r# is found by dividing a term by the previous term.

#r=(-10)/2 =-5color(white)(aaa)# #n=6color(white)(aaa)#and #a_1=2#

#S_n= frac(2*(1-(-5)^6))(1- -5)= frac(2*(1-15625))(6)=frac(2*-15624)(6)#

#S_n=-5208#

Alternatively, you could continue the sequence to 6 terms and add them.

First find the next 3 terms by multiplying the previous term by #r=-5#

#2, -10,50, -250, 1250, -6250#

Then add these 6 terms together. The sum is #=5208#