Question

Find 3 no of an Ap whose Sum is 15 & product is 45. let 3 terms are (a-d),a,a+d​

Answer 1

EXPLANATION.

Three numbers are in ap.

Sum of an ap = 15.

Products of an ap = 45.

As we know that,

Three numbers are in ap.

⇒ (a - d), a, (a + d).

Sum of an ap = 15.

⇒ a - d + a + a + d = 15.

⇒ 3a = 15.

⇒ a = 5.

Products of an ap = 45.

⇒ (a - d) x (a) x (a + d) = 45.

⇒ (a - d)(a + d) x (a) = 45.

⇒ (a² - d²) x (a) = 45.

Put the value of a = 5 in equation, we get.

⇒ [(5)² - d²] x (5) = 45.

⇒ [25 - d²] = 9.

⇒ 25 - d² = 9.

⇒ - d² = 9 - 25.

⇒ - d² = - 16.

⇒ d² = 16.

⇒ d = √16.

⇒ d = ± 4.

Case = 1.

First term = a = 5.

Common difference = d = 4.

⇒ (a - d), (a), (a + d).

Put the values in the equation, we get.

⇒ (5 - 4), (5), (5 + 4).

⇒ 1, 5, 9

Three numbers are : 1, 5, 9.

Case = 2.

First term = a = 5.

Common difference = d = - 4.

⇒ (a - d), (a), (a + d).

Put the values in the equation, we get.

⇒ [(5) - (-4)], (5), [5 + (-4)].

⇒ [5 + 4], [5], [5 - 4].

⇒ 9, 5, 1.

Three numbers are : 9, 5, 1.