Question

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

Answer 1

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