find the values of p and q in the arithmetic progression: -12,p,q,18.

the common difference is 10
... there are three differences from -12 to 18
... (18 - -12) / 3 = 10

-12 , -2 , 8 , 18

q - p = d
18 - q = d
p + 12 = d
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so q = 18-d and p = d - 12
so (18-d) - ( d-12) = d
30 - 2 d = d
d = 10
q = 18 - 10 = 8
p = 8 -10 = -2
so
-12 , -2 , 8 , 18

Correct

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