What is the sum of the arithmetic sequence 153, 139, 125, …, if there are 22 terms?

1 Answer
May 22, 2018

#6600#

Explanation:

First, find the value of #a#. The value of #a# is the first term in the sequence you've been given. This progression does not succeed, it reduces with every term.

Therefore, #a=153#

Then find the difference between the values you have been given. Knowing that this is an arithmetic sequence, the difference #d# between the values should be equal. You can find this by subtracting the first and second value away from each other like so:

#153-139=14#
#139-125=14#

Therefore, #d=14#

We also have been told that there are #22# terms. This is the value of the #nth# term.

#n=22#

Now the sum of all the terms in the arithmetic sequence can be found by substituting in the values for #n#, #d# and #a#:

#Sn = (n/2)(2a+(n-1)d)#

#Sn = (22/2)((2*153)+(22-1)*14)#

#Sn = 11(306+294)#

#Sn = 6600#