SOLUTION: The odd integers are arranged into sets, each succeeding set continuing from the previous, and containing one more number as follows: {1},{3,5},{7,9,11},{13,15,17,19},... what is t

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Question 1147618: The odd integers are arranged into sets, each succeeding set continuing from the previous, and containing one more number as follows: {1},{3,5},{7,9,11},{13,15,17,19},... what is the sum of the numbers in the 22nd set?
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The number of numbers in the first 21 sets is

1+2+3+...+20+21 = (21*22)/2 = 231

The numbers in the 22nd set are the 22 odd numbers starting with the 232nd odd number -- i.e., the 232nd through the 253rd odd numbers.

So the sum of the numbers in the 22nd set is

463+465+...+505 = 22*((463+505)/2) = 11*968 = 10648

Another path to the answer, after finding the answer is the sum of the 232nd through the 253rd odd number....

The sum of the first n odd numbers is n^2. So the sum of the 232nd through 253rd odd number is the sum of the first 253 odd numbers minus the sum of the first 231 odd numbers:

253^2-231^2 = 10648
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The odd integers are arranged into sets, each succeeding set continuing from the previous, and containing one more number as follows: {1},{3,5},{7,9,11},{13,15,17,19},... what is the sum of the numbers in the 22nd set?
Sum of 1st set: 1

Sum of 2nd set: 8

Sum of 3rd set: 27

Sum of 4th set: 64

With set number being n, and based on above observation, sequence is: n3

Based on the 4 sets, we get: 

Therefore,  

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