Question

What are three consecutive integers whose sum is \[87\] ?

Answer 1

Hint: Consecutive Integers follow a sequence where each number is one more than the previous number. We have to find three numbers which are consecutive and their addition leads to \[87\] for which we will use the simple addition formula.

Complete step-by-step answer:
Consecutive means unbroken or continuing, hence consecutive integers means following a series in which each subsequent number is one higher than the previous number. For example, following are consecutive integers:
 \[1,2,3,4,5,....\]
The formula to get consecutive integer is:
 \[n + 1\]
Where \[n\] is an integer.
We can solve the sum as follows by forming an equation comparing with above formula:
 \[ \Rightarrow n + (n + 1) + (n + 2) = 87\]
Here \[(n + 1)\] is consecutive integers of \[n\] and \[(n + 2)\] is consecutive integers of \[(n + 1)\] respectively and they make up three consecutive integers whose sum is \[87\] .
Now opening up the brackets,
 \[ \Rightarrow n + n + 1 + n + 2 = 87\]
Adding the numbers on LHS,
 \[ \Rightarrow 3n + 3 = 87\]
Subtracting \[3\] on the RHS,
 \[ \Rightarrow 3n = 87 - 3\]
 \[ \Rightarrow 3n = 84\]
Dividing by \[3\] on the RHS,
 \[ \Rightarrow n = \dfrac{{84}}{3}\]
Hence, we get the first integer as:
 \[ \Rightarrow n = 28\]
Now to find out the remaining two integers by substituting the value of \[n\] -
Second integer:
 \[ \Rightarrow n + 1 = 28 + 1 = 29\]
Third integer:
 \[ \Rightarrow n + 2 = 28 + 2 = 30\]
Hence the three consecutive integers whose sum will be equal to \[87\] are \[28,29\] and \[30\]
So, the correct answer is “28, 29, AND 30”.

Note: We can verify the solution by adding the numbers i.e. \[28 + 29 + 30 = 87\] . We should re-verify the solution in such types of sums.
The mean and median of a given set of consecutive integers is equal. In the given sum it will be:
 \[\dfrac{{87}}{3} = 29\]
The formula to get consecutive odd integer is:
 \[2n + 1\]
E.g. The consecutive odd integer after \[1\] will be-
 \[2(1) + 1 = 2 + 1 = 3\] .
The formula to get consecutive odd integer is:
 \[2n\]
 E.g. The consecutive even integer after \[2\] will be –
 \[2(2) = 4\]