Question

.the sum of three consecutive terms that are in a. p is 27 and their product is 288. find the three terms.

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Answer 1

Answer:

Let the three consecutive terms be a – d, a, a + d

Their sum = a – d + a + a + d = 27 3a = 27 a = 27/3 = 9

Their product = (a – d)(a)(a + d) = 288 = 9(a2 – d2) = 288 ⇒ 9(9 – d2) = 288

⇒ 9(81 – d2) = 288 81 – d2 = 32 -d2 = 32 – 81 d2 = 49 ⇒ d = ± 7

∴ The three terms are if a = 9, d = 7 a – d, a , a + d = 9 – 7, 9 + 7 A.P. = 2, 9, 16 If a = 9, d = -7 A.P. = 9 – (-7), 9, 9 + (-7) = 16, 9, 2

Answer 2

Step-by-step explanation:

Let the three consecutive terms be a – d, a, a + d Their sum = a – d + a + a + d = 27 3a = 27 a = 27/3 = 9 Their product = (a – d)(a)(a + d) = 288 = 9(a2 – d2) = 288 ⇒ 9(9 – d2) = 288 ⇒ 9(81 – d2) = 288 81 – d2 = 32 -d2 = 32 – 81 d2 = 49 ⇒ d = ± 7 ∴ The three terms are if a = 9, d = 7 a – d, a , a + d = 9 – 7, 9 + 7 A.P. = 2, 9, 16 If a = 9, d = -7 A.P. = 9 – (-7), 9, 9 + (-7) = 16, 9, 2Read more on Sarthaks.com - https://www.sarthaks.com/935583/the-sum-three-consecutive-terms-that-are-in-27-and-their-product-is-288-find-the-three-terms