Given the sum of the first 85 positive even integers is 7,310 , what is the sum of the first 85 positive ODD integers?

Answer 1

We'll write the two sums down.

The sum of positive odd integers, we'll say equals x.

2 + 4 + 6 + 8 + ... = 7310

1 + 3 + 5 + 7 + ... = x

Notice that every number in the odd sum is one less than the corresponding number in the even sum.

Answer 2

Well the first 85 positive even integers are 2, 4, 6 , ..... 2 x 85

first positive odd 1, 3, 5, ..... 2 x 85 - 1

There are the same number of integers and each integer in the 2nd list is one less than the corresponding integer in the first

So total = total of first list - 85 x 1 = 7310 - 85