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Arithmetic Progression

The sum of fi...

Question

The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. find the AP.

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Solution

let the first 3 terms of the A.P be a-d, a and a+d

by data, (a-d) + a + (a+d)= 48

3a=48

a=16

as per data: (a-d)a= 4(a+d)+12--(1)

substituting the value of 'a' in (1); (16-d)16=4(16+d) +12

256 - 16d = 64 + 4d + 12

256 - 16d =76 + 4d

256-76= 16d+4d

180 = 20d

d= 9

therefore the A.P is : 16, 25, 34...

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