How do you find the sum of the arithmetic sequence 2 + 5 + 8 + ... + 53?

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Answer 1 · 2016-08-21T08:18:34

The sum of this sequence is #495#.

To find the sum of an arithmetic sequence we use the following formula:

#S_n=(a_1+a_n)/2*n#

First we need to find the number of terms #n#. To do this we use the #n-th# term formula:

In the question we have:

#a_n=53#, #a_1=2#, #r=3#

#53=2+(n-1)*3#

#51=3*(n-1)#

#n-1=17#

#n=18#

Now we can calculate the sum:

#S_18=(2+53)/2*18=55*9=495#

Answer: The sum of this sequence is #495#