What is the sum of the arithmetic sequence 174, 168, 162 …, if there are 37 terms?

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Answer 1 · 2016-03-24T07:53:44

Sum of the series is #2442#

Sum of an Arithmetic series

#{a,(a+d),(a+2d),...(a+(n-1)d)}# up to #n# terms is given by

#n/2xx(2a+(n-1)d)#

where #a# is the first term and #d# is the difference between a term and its preceding term.

Here first term #a=174# and #d=168-174=-6# and #n=37#

Hence the desired sum is #37/2xx{2xx174+(37-1)xx(-6)}# or

#37/2xx(348-36xx6)# or #37/2xx(348-216)# or

#37/2xx132=2442#