Calculate the sum 1+4+7+....+31.

Here

First term(a)=1

last term(b)=31

common difference(d)=4-1=3

we have,

tn=a+(n-1)d.....(where n=no. of terms)

b=a+(n-1)d 

31=1+(n-1)3

.

.

n=11

Thus, 31 is the 11th term.

Now, sum of 11 terms of the given A.S(Sn)

=n/2*(a+b)

=11/2*(1+31)

=11/2*32

=11*16

=176

thus, the sum of n terms, in this case all of them, is 176.