Answers

2015-09-20T10:32:03+08:00
My answer is P=1/2 To get it, I subtracted the second term and the 1st term.
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If P=1/2, then given P=#, 3P+2, and P+5 will no be an arithmetic sequence :-) You may check by substituting your solution to P.
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2015-09-22T16:11:57+08:00

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1) Find the difference between each term:
   a) (P + 5) - (3P + 2)
       = (P + 5) + (-3P - 2) - To subtract polynomial, change the signs of eacht
                                       term in subtrahend, then proceed to addition
       = -2P + 3, difference between third and second terms
  
    b) (3P + 2) - (P + 3)
        = (3P + 2) + (-P - 3)
        = 2P - 1, the difference between second and first terms

2) Equate the difference between the terms,  since this is an arithmetic sequence where the difference between each term is equal.
 
2P - 1 = -2P + 3
2P + 2P = 3 + 1
4P = 4
4P/4 = 4/4
P = 1

To check, substitute 1 for P:
P + 3 = 1 + 3 = 4
3P + 2 = 3(1) + 2 = 3 + 2 = 5
P + 5 = 1 + 5 = 6

Arithmetic sequence: 4, 5, 6
Common difference: 1


   

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