15. Find three numbers a,b,c between 2 and 18 such that (i) their sum

1.	15. Find three numbers a,b,c between 2 and 18 such that (i) their sum is 25 (i) the num2,a,b are consecutive terms of an A.P. (iilithe numbers b, c, 18 are consecutive terms of
Answer» 2 < a, b, c, < 18 a + b + c = 25 ……. (1) 2, a, b are AP ⇒ 2a = b + 2 ⇒ 2a – b = 2 …….. (2) b, c, 18 are in GP ⇒ c2= 18b …… (3) From (2) ⇒ a = b +2/2 (1) ⇒ b + 2/2 + b + c = 25 ⇒ 3b = 48 – 2c (3) ⇒ c2= 6 (48 – 2c) ⇒ c2+ 12c – 288 = 0 ⇒ c = 12, - 24 (rejected) ⇒ a = 5, b = 8, c = 12

15. Find three numbers a,b,c between 2 and 18 such that (i) their sum is 25 (i) the num2,a,b are consecutive terms of an A.P. (iilithe numbers b, c, 18 are consecutive terms of

Answer»

2 < a, b, c, < 18 a + b + c = 25 ……. (1)

2, a, b are AP ⇒ 2a = b + 2

⇒ 2a – b = 2 …….. (2)

b, c, 18 are in GP ⇒ c2= 18b …… (3)

From (2) ⇒ a = b +2/2

(1) ⇒ b + 2/2 + b + c = 25 ⇒ 3b = 48 – 2c

(3) ⇒ c2= 6 (48 – 2c) ⇒ c2+ 12c – 288 = 0

⇒ c = 12, - 24 (rejected)

⇒ a = 5, b = 8, c = 12