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The product of the first and the third terms of an arithmetic sequence is 9. If all terms of the sequence are positive integers, what is the fourth term?

 Nov 3, 2021
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The product of the first and the third terms of an arithmetic sequence is 9. If all terms of the sequence are positive integers, what is the fourth term?     

 

What different integers can be multiplied to get 9?  Only (1 x 9) and (3 x 3). 

3 and 3 isn't a sequence, so it has to be 1 and 9. 

And the first number has to be 1 because all terms of the sequence are positive. 

If 9 were the first number, they'd be decreasing and get into the negative numbers. 

 

Halfway between 1 and 9 is 5 so we know the sequence is add 4 to each previous number.  

 

So the sequence is 1,  5,  9,  13,  17,  etc. and as we can see, 13 is the fourth term.  

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 Nov 3, 2021

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