What is the least of these integers if the average of five consecutive odd integers is -21.

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Jade Mejia · Accepted Answer

Take x. This is the smallest integer. Since these are consecutive odd integers, the second must be 2 greater than the first. The third number must be 2 greater than the second. And so forth.For example, 1,3,5,7,and9 are five consecutive odd integers, and they are all two more than the last. So, our five numbers arex,x+2,(x+2)+2,((x+2)+2)+2,and(((x+2)+2)+2)+2which meansx,x+2,x+4,x+6,andx+8According to the question, their average is −21. So,x+(x+2)+(x+4)+(x+6)+(x+8)5=−21Therefore, by simplifying,5x+205=−21So5x+20=−105Then5x=−125andx=−25Shortcut: Since these are odd integers that are consecutive, you can take −21 as the middle number, −23 as the second, −19 to even out the −23 and maintain the average of −21, then −25 as the first, then −17 as the last. This is a little hard to explain but makes sense if you really think about it.

What is the least of these integers if the average of five consecutive odd integers is -21.

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