Question

find the sum of all the odd numbers from the least three digit number to the highest 3 digit number​

Answer 1

We know that the least odd 3 digit number is 101 and the highest is 999.

Now let a, d and n be the first term, common difference and no of terms of the AP so formed.

Thus we have,
a =101
d =2 (two consecutive odd number occur at a difference of 2)
l (last term) = 999

Now, l = an = 999
=> a+(n-1)d = 999 [an = a+(n-1)d ]
=> 101 + (n-1)2 = 999
=> (n-1)2 = 898
=> n-1 = 449
=> n = 450

Thus there are a total of 899 terms in the AP.

Now, Sn = Sum of n terms
= n/2(a+l)
= 450/2(101+999)
= 450/2(1100)
= 247500

Answer 2

this is the answer for the question