How do you find the sum of the arithmetic sequence given 4 + 1 + –2 + –5 + –8 + –11?

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Answer 1 · 2016-07-21T07:25:49

#S_n=n/2(11-3n)#.

#S_6=-21#.

Let #a, d & S_n# denote the #1^(st)# term, the common difference and the sum of its first #n# terms, resp.

Then, we know that,

#S_n=n/2{2a+(n-1)d}#.

Here, we have #a=4, d=1-4=-3

Hence, #S_n=n/2{8-3(n-1)}=n/2(8-3n+3)=n/2(11-3n)#

Referring to our reqd. sum, #n=6#, so that,

#S_6=6/2(11-3xx6)=3(11-18)=3(-7)=-21#.