How do you find the sum of the arithmetic sequence given 26+19+12+5+....(-37)?

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Answer 1 · 2016-05-26T15:17:30

The sum of the arithmetic sequence #=-55#

The arithmetic sequence provided is :
#26 + 19 + 12 + 5 + ......-37#

The first term: #a_1 = 26#
The common difference for the sequence can be found as follows:
#a_2 - a_1 = 19 - 26 =-7#
#color(blue)(d =-7#
The last term #a_n = -37#

We can find the total number of terms #(n)# of the series by using the formula:
#color(blue)(a_n = a_1 + ( n-1)d#

#-37 = 26 + ( n-1) xx color(blue)((-7))#

#-37 = 26 -7n + 7#

#-37 = 33-7n #

#7n = 33 + 37#

#7n = 70#

#n = 10#

Now we find the sum of the terms applying the below mentioned formula:

#color(green)(S_n = n/2 (a_1 + a _n)#

#=10/2 ( 26 +(-37)) #

#=5 xx (-11)#

#=-55#