How do you find the 25th partial sum of the arithmetic sequence #2, 8, 14, 20,...#?

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Answer 1 · 2018-04-28T01:32:01

See below

Using the sum formula #S_n= n/2(a_1+a_n)#

To figure out the 25th partial sum, it is essential to know it is just the sum of the first 25 numbers of the sequence.

We already have #n=25#
and #a_1=2#

To figure out #a_n# for the formula above, which is #a_25# in this case, we must write a rule:

Just by looking at the sequence we know the common difference is #6#

To write an explicit arithmetic rule:
#a_n= a_1+d(n-1)#
#a_n= 2+6(n-1)#

To solve for the 25term:
#a_25= 2+6(25-1)#
#a_25= 146#

Now to find the sum:
#S_25= 25/2(2+146)= 1850#