Question

how to quickly add odd numbers from 111to 131​

Answer 1

hi mate!!!

here is the trick!

Solution:

first,

let the first term= a= 111 and the last term= tn= 131.

d= common difference= 2

according to the formula,

tn= a+(n-1)×d

131= 111+(n-1)× 2

131= 111+ 2-2n

131= 111-2+2n

131= 109+2n

131-109= 2n

22= 2n

22/2= 11= n

hence,

there are 11 such numbers.

now,

their sum=

Sn=n/2×[2a+(n-1)×d]

=11/2×222+(10) ×2

=11/2× 222+ 20

=11/2× 242

= 11× 121

=1331

hence,

the sum= 1331

hope this helps!! ✌❤☺