SOLUTION: The sum of three consecutive terms of an A.p is 6, while their product is -90, find the common difference.

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Question 1110320: The sum of three consecutive terms of
an A.p is 6, while their product is -90, find the
common difference.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "a" be the middle term of the sequence, so that the three terms are


    a-d, a, a+d,


where d is the common difference of the AP.  Then


   (a-d) + d + (a+d) = 6,


which implies  3a = 6,  a = 2.


Then the second condition becomes


    (a-d)*a*(a+d) = -90,   or


    2*(2-d)*(2+d) = -90,

    4-d^2 = -45  ====>  d^2 = 4 + 45 = 49  ====>  d = +/-sqrt%2849%29 = +/-7.


So, the AP is   2-7 = -5,  2,   2+7 = 9,     OR

                2+7 =  9,  2,   2-7 = -5.

Solved.