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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?

 Aug 3, 2022
 #1
avatar+113 
+3

I think it is 13. In an Arithmetic Sequence the difference between one term and the next is a constant.

So if we imagine the first number is 1 and then the third is 9, we have these three numbers 1, 5, 9...

We see that there is a jump of 4 every time, so the sequence becomes...

1, 5, 9, 13, 17, 21 ....

See: https://www.mathsisfun.com/algebra/sequences-sums-arithmetic.html

 Aug 3, 2022
edited by tuffla2022  Aug 3, 2022
edited by tuffla2022  Aug 3, 2022
 #2
avatar+124596 
+1

Let the first term  = n

 

Let the third  =  n + 2d

 

So

 

n (n + 2d)  =  9

 

We have two  different (positive) factors that multiply to 9  →  1  and  9  

 

So  if   n =  1     and  d = 4   then

 

1 ( 1 + 8)  = 9

 

1 (9)  = 9

 

So the 4th term is    1 + 4(4 -1)  =  1 + 12  =  13

 

 

cool cool cool

 Aug 3, 2022
edited by CPhill  Aug 3, 2022

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