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

6 Answers

ayush01's profile pic

ayush01 | Student, Grade 10 | (Level 1) Honors

Posted on

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.

aj11's profile pic

aj11 | Elementary School Teacher | (Level 1) eNoter

Posted on

If you see carefully, you can find that this is the sum of arithmetic sequence by the number of 3

The sum of arithmetic sequence is  n/2*(a+L) {n=number of term ,a=first term ,L=last term)

Then.10/2 * ( 1 + 31 )=5 * 32 = 160