SOLUTION: p, q and r are three consecutive terms of an AP. express p and r in terms of q and d, where d is the common difference. If The Sum Of the terms is 21 and p=6r, find p, q and r.

Algebra ->  Sequences-and-series -> SOLUTION: p, q and r are three consecutive terms of an AP. express p and r in terms of q and d, where d is the common difference. If The Sum Of the terms is 21 and p=6r, find p, q and r.      Log On


   

Question 1148016: p, q and r are three consecutive terms of an AP. express p and r in terms of q and d, where d is the common difference. If The Sum Of the terms is 21 and p=6r, find p, q and r.
Answer by greenestamps(13200) About Me  (Show Source):
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In general in an AP, the first of three consecutive terms is the middle term minus the common difference and the third term is the middle term plus the common difference:

p = q-d
r = q+d

Also in general in an AP, the middle of three consecutive terms is the average of the three terms.

So, given in this problem that the sum of the three consecutive terms is 21, the middle term q is 7. Then

p = 7-d
r = 7+d

And the problem tells us p = 6r:

7-d+=+6%287%2Bd%29
7-d+=+42%2B6d
-35+=+7d
d+=+-5

So

p = q-d = 7-(-5) = 12
q = 7
r = 7+d = 7+(-5) = 2

ANSWER: The three terms are 12, 7, and 2.