1.

The sum of three terms in A.P. is 125 and their product is 45.Find the numbers.​

Answer»

Correct Question: The sum of three TERMS in A.P. is 15 and their product is 45.Find the numbers.

GIVEN:

Sum of three terms in AP = 15

Product of those three terms = 45

TO FIND:

Those three terms of AP

SOLUTION:

Let the numbers be (a - d), a and (a + d)

= > (a - d) + a + (a + d) = 15 \\ \\ = > a - d + a + a + d = 15 \\ \\ = > 3a = 15 \\ \\ = > a = \frac{15}{3} \\ \\ = > a = 5

Now,

= > (a - d) a (a + d) = 45 \\ \\ = > a( {a}^{2} - {d}^{2} ) = 45 \\ \\ = > 5( {5}^{2} - {d}^{2} ) = 45 \\ \\ = > (25 - {d}^{2} ) = \frac{45}{5} \\ \\ = > 25 - {d}^{2} = 9 \\ \\ = > - {d}^{2} = 9 - 25 \\ \\ = > - {d}^{2} = - 16 \\ \\ = > d = \sqrt{16} \\ \\ = > d = 4

Substitute (a) and (d) to find the numbers.

= > a - d = 5 - 4 = 1 \\ \\ = > a = 5 \\ \\ = > a + d = 5 + 4 = 9

THEREFORE, the numbers are 1, 5 and 9.


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