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

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