Question

How do you find 3 consecutive odd integers where the sum is \[ - 141\]?

Answer 1

Hint: In the given question, we have been given that there are three consecutive odd integers. Their sum is given to be \[ - 141\]. We have to find the value of the integers. To do that, we express the three integers in the form of a single integer – we are going to assume the value of one integer and express the others in the form of that one integer. And then we solve and find the value of the integers

Complete step by step answer:
Let the middle odd integer be \[x\].
Then, since the other two corners, odd integers are consecutive, they are equal to \[x - 2\] and \[x + 2\].
Now, we have the three numbers: \[x - 2,x,x + 2\].
Given, their sum is \[ - 141\].
Hence, \[x - 2 + x + x + 2 = - 141 \Rightarrow 3x = - 141 \Rightarrow x = - 47\]
So, the middle number is \[ - 47\].
Thus, the other two numbers are \[ - 47 - 2 = - 49\] and \[ - 47 + 2 = - 45\]

Hence, the three numbers are \[ - 49, - 47, - 45\].

Additional Information:
This system of the given numbers, where the difference between three or more numbers is equal is called an arithmetic progression. The arithmetic progression is used in such things only, for finding the integers when the numbers are quite big, and when we have to find the sum of such integers.

Note:
In the given question, we had to find the value of the three consecutive integers whose sum is given. To do that, we assumed the value of one integer and expressed the others in the form of that one integer. And then we solved and found the value of the integers. So, it is really important that we know the formulae and where, when, and how to use them so that we can get the correct result.