Question

the sum of three continuous odd numbers is 57 the middle one is,​

Answer 1

Answer:

The middle number is 19.

Step-by-step-explanation:

Let the middle odd number be x.

∴ First odd number = x - 2

Third odd number = x + 2

From the given condition,

The sum of three continuous odd numbers is 57.

∴ x - 2 + x + x + 2 = 57

⇒ x + x + x + 2 - 2 = 57

⇒ 3x = 57

⇒ x = 57 / 3

⇒ x = 19

∴ The middle number is 19.

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Verification:

We have, x = 19

∴ First odd number = x - 2 = 19 - 2 = 17

Third odd number = x + 2 = 19 + 2 = 21

Now,

Sum of three numbers = 17 + 19 + 21

⇒ Sum of three numbers = 10 + 7 + 10 + 9 + 20 + 1

⇒ Sum of three numbers = 10 + 10 + 20 + 9 + 1 + 7

⇒ Sum of three numbers = 40 + 10 + 7

⇒ Sum of three numbers = 50 + 7

⇒ Sum of three numbers = 57

It is given that the sum of three odd numbers is 57.

Hence verified!

Answer 2

Given that, the sum of three continuous odd numbers is 57.

We need to find the middle term.

▪︎Solution :

Let the middle odd number be x.

We know that, consecutive odd numbers have a difference of 2.

So,

• First odd number = x - 2
• Third odd number = x + 2

According to the Question,

=》 x - 2 + x + x + 2 = 57

=》 3x = 57

=》 x = 19

Hence, The middle number is 19.

▪︎Verification :

• First odd number = x - 2 = 17.
• Second odd number = x = 19.
• Third odd number = x + 2 = 21

Sum of three numbers = 17 + 19 + 21 = 57.

Hence, Verified.