SOLUTION: Find p so that the numbers 7p + 2, 5p +12, 2p -1,... form an arithmetic sequence. A. -8 B.-5 C. -13 D. -23

Question 982374: Find p so that the numbers 7p + 2, 5p +12, 2p -1,... form an arithmetic
sequence.
A. -8 B.-5 C. -13 D. -23
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe your solution will be p = -23
when p = -23:
A1 = 7*-23+2 = -159
A2 = 5*-23+12 = -103
A3 = 2*-23-1 = -47
the difference between A2 and A1 is (-103) - (-149) = 56
the difference between A2 and A3 is (-47) - (-103) = 56
in this arithmetic series, the common diffence is 56.
how was this derived?
take A2 - A1 and you get the difference between them.
(5p + 12) - (7p + 2) = (-2p + 10)
take A3 - A2 and you get the difference between them.
(2p-1) - (5p + 12) = (-3p - 13)
since the difference between each element in an arithmetic series must be the same, then set (-2p + 10) equal to (-3p - 13) and solve for p.
when you do that, you will get p = -23.

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