Question

The sum of three numbers in ap is 27 and thir products is 405 . Find the numbers

Answer 1

Solution :

Let ( a - d ), a , ( a + d ) are three

numbers in A.P

i ) sum = 27

=> a - d + a + a + d = 27

=> 3a = 27

=> a = 27/3

=> a = 9 ---( 1 )

ii ) product = 405

=> ( a - d ) × a × ( a + d ) = 405

=> ( a² - d² ) a = 405

=> ( 9² - d² ) × 9 = 405

=> 81 - d² = 405/9

=> 81 - d² = 45

=> -d² = 45 - 81

=> - d² = - 36

=> d² = 6²

=> d = ± 6

Therefore ,

1 ) if a = 9 , d = 6

Required 3 terms are

a - d = 9 - 6 = 3

a = 9

a + d = 9 + 6 = 15

2 ) if a = 9 , d = -6

required 3 terms are

15 , 9 , 3

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