What is the sum of the arithmetic sequence 135, 123, 111 …, if there are 34 terms?

1 Answer
Feb 13, 2016

Answer:

Sum of the sequence is #-4284#.

Explanation:

We have to find the sum of arithmetic sequence #{135, 123, 111 …}# up to 34 terms.

In the sequence #a_1, a_2, a_3, .... ... ,a_n# nth term is given by #a_1+(n-1)d# where #a_1# is the first term #d# is the constant difference (a_2-a_1). Here #a_1# is #135# and #d=-12#, hence

#a_34 = 135+33*(-12)= 135-396 = -261#.

Sum of the series is given by #n(a_1+a_n)/2# and in this case it turns out to be #34*(135-261)# or #34*(-126)# or #-4284#-