Question

What is the sum of each of following pair of number ;1 and 100,2 and 99,3 and 98 ,4 and 97 and so on fourth until you reach 50 and 51?

Answer 1

This AP terms can be added either by using AP laws & formulae…. Like the Sum of the terms of AP, Sn = n/2 { a+ l}

OR any such AP terms can be added by associating the terms in pairs , picked from the begining & from the end, in the following way… And this method is actually the derivation of the formula of the sum of n terms.

(1+99) + (2+98) +(3+97) ……( 49+ 51)……49times

49 times because 99/2 = 49.5( integral part)

Here 50 is not paired with any number, so it will be added separately…

= 100 x 49 = 4900

4900 +50 = 4950

= 4950 ………ANS