The sum of three terms of an A.P. is 21 and the product of the first a

1.	The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.
Answer» Let’s consider the three terms of the A.P. to be a – d, a, a + d so, the sum of three terms = 21 ⇒ a – d + a + a + d = 21 ⇒ 3a = 21 ⇒ a = 7 And, product of the first and 3rd = 2nd term + 6 ⇒ (a – d) (a + d) = a + 6 a² – d² = a + 6 ⇒ (7 )² – d² = 7 + 6 ⇒ 49 – d² = 13 ⇒ d² = 49 – 13 = 36 ⇒ d² = (6)² ⇒ d = 6 Hence, the terms are 7 – 6, 7, 7 + 6 ⇒ 1, 7, 13

The sum of three terms of an A.P. is 21 and the product of the first and the third terms exceeds the second term by 6, find three terms.

Answer»

Let’s consider the three terms of the A.P. to be a – d, a, a + d

so, the sum of three terms = 21

⇒ a – d + a + a + d = 21

⇒ 3a = 21

⇒ a = 7

And, product of the first and 3rd = 2nd term + 6

⇒ (a – d) (a + d) = a + 6

a² – d² = a + 6

⇒ (7 )² – d² = 7 + 6

⇒ 49 – d² = 13

⇒ d² = 49 – 13 = 36

⇒ d² = (6)²

⇒ d = 6

Hence, the terms are 7 – 6, 7, 7 + 6 ⇒ 1, 7, 13