What is the sum of the arithmetic sequence 140, 134, 128…, if there are 33 terms?

1 Answer
Apr 10, 2016

Answer:

We first work out the 33th term, the general formula for a sequence like this being #a_n=a_0+nxxd#, #d# being the difference.

Explanation:

Every term is the previous plus or minus the differnce #d=-6#. So to get to the 33th term we take 32 of these steps (remember we call the first term #a_0# and the 33th is thus #a_32# -- remember this!!):

#a_32=140+32xx(-6)=-52#

The sum is #33xx# the average, or

#sum=33xx(140+(-52))/2=33xx88/2=1452#