The sum of the first n consecutive positive odd integers is

Hi All,

These types of "sum of a sequence" questions can be approached in a number of different ways - you can use various formulas or you can approach this prompt by pattern-matching and minimizing the math that you have to do. For this question, you can use "bunching"....

We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 13 to 39, inclusive. We're asked for the SUM of this group.

1) Start with the sum of the smallest and the biggest: 13 + 39 = 52
2) Now look at the 'next smallest' and the 'next biggest': 15 + 37 = 52

From this, you can see that you're just going to be adding up a bunch of 52s. We DO have to check to see if there's a "middle" term in this sequence that doesn't get "bunched" though. To determine if that middle term exists, we just have find the last few 52s in the group....

21 and 31
23 and 29
25 and 27

Now we have proof that there is no middle term. We have 7 bunches of 52.

7(52) = 364

Final Answer:

GMAT assassins aren't born, they're made,
Rich

13 & 39 inclusive

sum must be sum upto 39-sum upto 11

11 is (11+1)/2=6th term

39 is 20th term

20^2-11^2=364

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