Question

the sum of three number in AP is 15 and the product of first and the last is 21 find the number​

Answer 1

Answer

Let the numbers = (a-d), a, (a+d)

Sum = a - d + a + a - d = 15

=> 3a = 15

=> a = 5

Product = (a-d)(a+d) = 21

=> a^2 - d^2 = 21

=> d^2 = 4

=> d = 2, -2

Numbers = 3, 5, 7 / 7, 5, 3

Answer 2

GIVEN

A.P. = (a - d) ,( a ), (a + d)

Here being increased by d

Their Sum = 15

Product of 1st and 3rd term = 21

TO FIND

The Terms

SOLUTION

1st Term + 2nd term +3rd Term = 15

=> a - d + a + a + d = 15

=> 3a = 15

=> a = 5 ... .eq.01

Now,

1st term × 3rd term = 21

=> (a - d)(a + d) = 21

=> a ^2 - d ^2 = 21

=> 5^2 - d^2 = 21 [from eq.01]

=> 25 - d^2 = 21

=> - d ^2 = - 4

=> d^2 = 4

=> d = 2 or - 2

so, the terms are (5 - 2) , (5) , (5 + 2)

or 5 - (-2) , 5, 5 + (-2)

THE AP IS 3 ,5 ,7 or 7,5,3