The sum of the first three terms of an AP is 30 while their product is 750. Find AP
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The sum of the first three terms of an AP is 30 while their product is 750. Find AP
a-d, a, a+d are the three terms of the AP.
Their sum a-d+a+a+d = 3a = 30, or
a = 30/3 = 10.
(a-d)(a+d)a = 750
a(a^2-d^2) = 750
10(100-d^2) = 750, or
100-d^2 = 75
d^2 = 100–75 = 25,
d = ± 5
So the three terms of the AP are 5, 10 and 15 or
15, 10 and 5.
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