Question

Find the sum of the odd numbers between 10 and 50

Answer 1

We need to find the sum of odd numbers between 10 and 50. 

The odd numbers from 10 to 50 go like 11, 13, 15......49

Thus forming an AP 11, 13, 15....49 (Where a=11, d=2, last term (an)= 49)

We know that an = a + (n-1) d

Putting values in the formula, 

49= 11 + (n-1) 2
49= 11 + 2n - 2
49= 9 + 2n
2n= 40
n= 40/2
n= 20

So now, substitute all the values in the formula Sn= n/2 (a + an)

Sn= 20/2 ( 11 + 49)
    = 10 ( 60)
    = 600 

Answer= 600 

Answer 2

see it's an arthematic progression known as A.P. with common difference 2
first term (a)=11
end term(l) =49
total number of terms (n)=25-5=20
so sum =n/2(a+l)
sum=20/2(11+49)
=600