Question

If the sum of three consecutive numbers in an A.P is 54
and their product is 5670 then find the three numbers.​

Answer 1

Let three consecutive number in an A.P are ; (a - d), a , (a + d)

given,

sum of numbers = 54

or, (a - d) + a + (a + d) = 54

or, 3a = 54

or, a = 18 .......(1)

again, product of numbers = 5670

or, (a - d)a(a + d) = 5670

or, (a³ - ad²) = 5670

from equation (1),

or, 18³ - 18d² = 5670

or, 5832 - 18d² = 5670

or, -18d² = 5670 - 5832

or, -18d² = -162

or, d² = 9

or, d = ±3

now when d = +3 , a = 18

(a - d) = 15

a = 18

(a + d) = 21

hence, three consecutive numbers are ; 15, 18, 21

and when d = -3 , a = 18

(a - d) = 21

a = 18

(a + d) = 15

hence, three consecutive numbers are ; 21, 18, 15 .

therefore, three consecutive numbers are ; 15, 18, 21 or 21, 18, 15

Answer 2

Answer:

hence, three consecutive numbers are ; 21, 18, 15

Explanation:

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