Question

3 numbers in Ap whose sum is 18 n product is 210 are

Answer 1

Given :-

Sum of the 3 terms of an A.P. is 18.

Product of the 3 terms of the A.P. is 210.

To find :-

The 3 terms.

Solution :-

Let the 3 terms be a - d, a and a + d.

A/q,

(a - d) + a + (a + d) = 18

⇒a + a + a - d + d = 18

⇒3a = 18

⇒a = 6

Again,

a(a - d)(a + d) = 210

⇒6(6 - d)(6 + d) = 210

⇒(6)² - (d)² = 35

⇒36 - d² = 35

⇒d² = 36 - 35

⇒d² = 1

⇒d = 1

Now, the three terms are :

• (a - d) = (6 - 1) = 5

• a = 6

• (a + d) = (6 + 1) = 7

Answer 2

Solutions:

Let the 3 terms be a - d, a , and a + d.

Now,

a - d + a + a + d = 18

3a = 18

a = 6

Putting the value of = a

a(a - d)(a + d) = 210

6(6 - d)(6 + d) = 210

(6)² - (d)² = 35

36 - d² = 35

d² = 36 - 35

d² = 1

d = 1

Therefore,

(a - d) = (6 - 1) = 5

a = 6

(a + d) = (6 + 1) = 7

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