if sum and product of three terms of an AP are 15 and 80 respectively then find the AP
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Step-by-step explanation:
a1 + a2 + a3 = 15
a1 × a2 × a3 = 80
let A.P be a - d, a, a + d
therefore,
a1 = a - d
a2 = a
a3 = a + d
a1 + a2 + a3 = a - d + a + a + d = 15
3a = 15
a = 5
a1 × a2 × a3 = 80
(a - d) × a × (a + d) = 80
as a = 5
(5 - d)(5 + d)(5) = 80
25 - d² = 80/5
25 - d² = 16
d² = 9
Case 1
a = 5
d = +3
AP: 2, 5, 8, 11......
Case 2
a = 5
d = -3
AP: 8, 5, 2 .....
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