The sum of three consecutive odd numbers is 57. Find the numbers. (a) 17, 19 and 21 (b) 19, 15 and 25 (c) 13, 17 and 26 (d) 21, 13 and 29
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.
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