Question

The sum of the first three numbers in an arithmetic progression is 18. If the product of the first and the third term is 5 times the common difference. Find the three numbers..

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Answer 1

Answer:

2, 6, 10

Step-by-step explanation:

Given The sum of the first three numbers in an arithmetic progression is 18. If the product of the first and the third term is 5 times the common difference. Find the three numbers.

Assume the three numbers as  a + d, a, a - d.

Given sum of 3 terms in an A P is equal to 18

So a + d + a + a - d = 18

   3 a = 18

    a = 6

Now again product of first and third term is 5 times common difference(d)

so (a + d)(a - d) = 5 d

 This is in the form of (a + b)(a - b) = a^2 - b^2

   a ^2 - d^2 = 5 d

  6^2 - d^2 = 5 d

   d^2 + 5 d - 36 = 0

  d^2 + 9 d - 4 d - 36 = 0

 (d + 9)(d - 4) = 0

  d = - 9, 4

Taking d = 4 we get 6 + 4 = 10, 6 - 4 = 2 and a = 6

So the numbers are 2, 6, 10