Find P So That The Numbers 7p+2, 5p+12, 2p-1 Form An Arithmetic Sequence., A. -8, B. -5, C. -13, D. -23

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:

D. -23

Step-by-step explanation:

Arithmetic sequences have a common difference (d) which may be obtained by subtracting a term with the term before it.

$d = a_{n} - a_{n-1}$

5p + 12 - (7p + 2) = 2p - 1 - (5p + 12)

5p - 7p + 12 - 2 = 2p - 5p - 1 - 12

-2p + 10 = -3p - 13

-2p + 3p = -10 - 13

p = -23

Checking:

p = -23

7p + 2 = -159

5p + 12 = -103

2p - 1 = -47

d = 56

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