How do you find the sum of the arithmetic sequence. -1, 2, 5, 8, 11, 14, 17?

1 Answer
Feb 23, 2016

Answer:

Just add them or use process as given below. Sum is #56#.

Explanation:

An arithmetic sequence is of type #a, a+d, a+2d, a+3d, ....#
in which first term is #a# and difference between a term and its preceding term is #d#.

#n^(th)# term of such a sequence is #a+(n-1)d# and sum of the series up to #n# terms is given by #an+n(n-1)d/2#

In arithmetic sequence. #{-1, 2, 5, 8, 11, 14, 17, .........}#, #a=-1# and #d=3#, hence of first #n# terms is #-n+(3n(n-1))/2#, whic can be simplified to #(-2n+3n^2-3n)/2# or

#(3n^2-5n)/2#.

As there are #7# terms in the series, their sum is #(3*7^2-5*7)/3# or #(147-35)/2# or #112/2# or #56#.