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Question

Answers

(a) 17, 19 and 21

(b) 19, 15 and 25

(c) 13, 17 and 26

(d) 21, 13 and 29

Answer
Verified

Hint: Here, we will first try to express the three consecutive odd numbers using a single variable n. After this we will equate their sum to 57 to find the value of n and also the values of three consecutive odd numbers.

Complete step-by-step answer:

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

So, we can say that the difference between any two consecutive odd numbers is:

= 2k+3 – (2k+1)

=2k+3-2k-1

=2

So, for every two consecutive odd numbers there is a difference of 2.

Now, let us take ‘n’ to be an odd number.

So, an odd number just before n will be (n-2).

And also an odd number just after n will be (n+2).

Since, it is given that the sum of these three consecutive odd numbers is 57. So, we can write the following equation:

n-2+n+n+2=57

3n=57

So, n = 19

The odd number before n will be = n -2 = 19-2 = 17

And the odd number after n will be = n+2 = 19 + 2 = 21

Therefore, the required three consecutive odd numbers are 17, 19 and 21.

Hence, option (a) is the correct answer.

Note: Here, the most important thing to note is that the difference between two consecutive odd numbers is 2. To avoid chances of mistakes the equations should be made carefully.

Complete step-by-step answer:

Since, we know that any odd number is always of the form (2k +1). We express an odd number in this form because we know that an odd number is not divisible by 2.

Now, the next odd number after (2k+1) will be (2k+3) because if we take (2k+2) then we can see that it is clearly divisible by 2.

So, we can say that the difference between any two consecutive odd numbers is:

= 2k+3 – (2k+1)

=2k+3-2k-1

=2

So, for every two consecutive odd numbers there is a difference of 2.

Now, let us take ‘n’ to be an odd number.

So, an odd number just before n will be (n-2).

And also an odd number just after n will be (n+2).

Since, it is given that the sum of these three consecutive odd numbers is 57. So, we can write the following equation:

n-2+n+n+2=57

3n=57

So, n = 19

The odd number before n will be = n -2 = 19-2 = 17

And the odd number after n will be = n+2 = 19 + 2 = 21

Therefore, the required three consecutive odd numbers are 17, 19 and 21.

Hence, option (a) is the correct answer.

Note: Here, the most important thing to note is that the difference between two consecutive odd numbers is 2. To avoid chances of mistakes the equations should be made carefully.

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