SOLUTION: Calculate the first ten term of an arithmetic progression whose 5th term is 24 and the difference between the 7th and 10th term is 15

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Question 1074129: Calculate the first ten term of an arithmetic progression whose 5th term is 24 and the difference between the 7th and 10th term is 15
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
Since there are only 10 terms, it's just as easy not to
use formulas, especially since we're going to have to
calculate all the terms:

Start with a5 = 24, subtract d each time for the 
terms before the 5th and add d each time for the
terms after 5th:


 a1 = 24-4d, 
 a2 = 24-3d, 
 a3 = 24-2d, 
 a4 = 24-d, 
 a5 = 24, 
 a6 = 24+d,
 a7 = 24+2d, 
 a8 = 24+3d,
 a9 = 24+4d, 
a10 = 24+5d 

a7 - a10 = (24+2d) - (24+5d) = 15
                 24+2d-24-5d = 15
                         -3d = 15
                           d = -5
                          

 a1 = 24-4d = 24-4(-5) = 24+20 = 44 
 a2 = 44+(-5) = 39 
 a3 = 39+(-5) = 34  
 a4 = 34+(-5) = 29 
 a5 = 24           <-- given, which checks, since 24=29+(-5) 
 a6 = 24+(-5) = 19
 a7 = 19+(-5) = 14 
 a8 = 14+(-5) = 9
 a9 =  9+(-5) = 4  
a10 =  9+(-5) = -1

Checking: a7 - a10 = 14-(-1) = 14+1 = 15

Edwin
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Calculate the first ten term of an arithmetic progression whose 5th term is 24 and the difference between the 7th and 10th term is 15
Depends! 

If the 10th term is greater than the 7th term, then d (common difference) is 5, and the 1st term or 

However, if the 7th term is greater than the 10th term, then d (common difference) is - 5, and the 1st term or 

So, there are 2 possible answers. 

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