Find the sum of the first 25 terms. 2,8,14,20

This is an arithmetic sequence as each term has a common difference to the previous term. Any arithmetic sequence can be expressed as:

a (n) = a+d (n-1), a=initial term, d=common difference, n=term number.

We know that a=2 and d = (20-14) = (14-8) = (8-2) = 6 so

a (25) = 2+6 (25-1)

a (25) = 146

The sum of an arithmetic sequence is the average of the first and last terms times the number of terms, in this case:

s (25) = 25 (2+146) / 2

s (25) = 1850

And if you care to remember the arithmetic sum formula it is:

s (n) = (2an+dn^2-dn) / 2, using a=2, d=6, and n=25 we get:

s (25) = (4 (25) + 6 (25^2) - 6 (25)) / 2

s (25) = 1850