the sum of 3numbers ib n AP is-3 and their po roduct is 8 . find them
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Let the numbers be a-r, a, a+r. (r being the common ratio)
Given
Sum of 3 numbers is -3.
(a-r) + a + (a+r) = - 3
3a = - 3
Therefore, a = -1
Also given that
Product of 3 numbers is 8.
(a-r)a(a+r) = 8
(a²-r²)a = 8
Substituting the value of a as -1 in above expression
(1-r²)(-1)= 8
(r²-1)= 8
r²= 9
r= ±3
Here we have two cases.
Case 1:
If r=+3
The numbers are - 4, - 1, 2.
Case 2:
If r=-3
The numbers are 2, - 1, - 4.
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