Math problem! please help me to solve this!?

Question

here's the question:

The set A consist of m consecutive integers with sum 2m. The set B consist of 2m consecutive integer with sum m. The difference between the largest element of set A and B is 2007. Find m.

the answer is 1338.

please explain it to me how to get this answer..

thank you very much

Answer 1

set A> in AP series

consecutive numbers > common difference =d=1

sum = 2m = (m/2)[2a + (m-1)*1]

2a + m-1 = 4

first term =a = (5-m)/2

largest term> last term = L1 = a + (m-1)*1 = (5-m)/2 + m-1 >>.find

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set B> in AP series

consecutive numbers > common difference =d=1

sum = m = (2m/2)[2b + (2m-1)*1]

2b + 2m-1 = 1

first term =b = (1-m)

largest term> last term = L2 = b + (2m-1)*1 = (1-m) + 2m-1 >>.find

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i could not do more on that, you just ensure whether last terms are largest > ELEMENTS in sets

L1-L2 = 2007 >> + ve difference

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you should get

3m/2 = 2007

m= 4014/3 = 1338

just just gave you hints