Find three number a, b, c between 2 and 18 such th

Question

Find three number a, b, c between 2 and 18 such that(i) their sum is 25(ii) the numbers 2, a, b sare consecutives terms of an A. P. and(iii) the numbers b, c, 18 are consecutive terms of a G. P.

Aditi Chauhan · Accepted Answer

Hello Student,

Please find the answer to your question

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

Thanks
Aditi Chauhan
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Algebra> Find three number a, b, c between 2 and 1...

Find three number a, b, c between 2 and 18 such that
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Find three number a, b, c between 2 and 18 such that(i) their sum is 25(ii) the numbers 2, a, b sare consecutives terms of an A. P. and(iii) the numbers b, c, 18 are consecutive terms of a G. P.

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