Evaluate each arithmetic series described?

Question

#sum^14 (4-10m)#
(below the #sum# is supposed to be m=5

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Answer 1 · 2018-05-30T02:07:17

The sum is #–910#.

We seek the sum #sum_(m=5)^14 (4-10m)#.

The sum of an arithmetic series with #n# terms is equal to #n# times the average of the first and last terms.

For this sequence, the first term is #4-10(5)=–46,# the last term is #4-10(14)=–136,# and the number of terms is #14-5+1=10.#

Thus, our sum is

#n xx ("first " + " last")/2#

#= 10 xx (–46+(–136))/2#

#=10xx(–91)#

#=–910#