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Question 28

The sum of the first and last of four consecutive odd integers is $$52$$. The sum of all of them is


Correct Answer: 104

Solution

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Let us assume the four odd integers as $$2n+1,2n+3,2n+5,2n+7$$. 

We are given that $$2n+1+2n+7=52$$, so $$4n+8 = 52 \implies 4n=44$$ or $$n =11$$

Thus the numbers are $$23,25,27,29$$

The sum of these numbers is 

$$23+25+27+29 =104$$

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