Problem Solving

The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
(A) 10,100
(B) 10,200
(C) 15,050
(D) 20,050
(E) 20,100

cindyqtran wrote:The sum of the first 100 positive integers is 5,050. What is the sum of the first 200 positive integers?
(A) 10,100
(B) 10,200
(C) 15,050
(D) 20,050
(E) 20,100

Given
1 + 2 + 3 ..... 100 = 5050

1+2 + 3 ..... 200 = 5050 + 101 + 102 ...... 200
=5050 + (1+100) + (2+100) + (3+100) ...... (100 +100)

= 5050 + 100*100 + 1 + 2+3.... 100
= 5050 + 10000 +5050

= 20100

sum of first 200 nos = n(n+1)/2 (where n is nos od the nos in series =200)

=200(201)/2 = 20100

and if someone does not know the series formulae here is how we shud solve..i assume we are not supposed to know the formula since they have given the sum of first 100 no's.

1+2+3...+100 = 5050
101=1+100
102=2+100
..........
199=99+100
200=100+100
thus sum of first 200 nos=sum of first 100+sum of first 100+(100*100)
=5050+5050+10000= the answer

Ya Gmatguy16 that's the reason why the sum of the first 100 nos is given.
I would personally solve it like u did, 5050 + 5050 +100 *100 (saves a lot of time)
just included the formula coz its really helpful in some problems.