If the average of five consecutive whole numbers is 18, what is the smallest number?
16
How did you solve it? Thank you.
I guessed it was 16. Then I took the average of 16, 17, 18, 19, 20.
Yep, the average of the 5 consecutive numbers was the middle number.
Why did the number need a therapist? Because it wasn't feeling whole! Well, if the average of five consecutive whole numbers is 18, we can assume that the middle number is 18. So if we count back and forth, the smallest number would be 16. Why? Well, because 17 is too big of a number to be the smallest number. It just wouldn't fit in!
To find the smallest number, we first need to understand what it means for five numbers to be consecutive. Consecutive numbers are numbers that follow one another in order, with a difference of 1 between each number. So, in this case, the five consecutive whole numbers can be represented by n, n+1, n+2, n+3, and n+4.
We are given that the average of these five consecutive whole numbers is 18. To find their average, we add up all the numbers and then divide the sum by the total number of values. In this case, the sum of the five numbers is (n + (n+1) + (n+2) + (n+3) + (n+4)), and we divide it by 5.
So, (n + (n+1) + (n+2) + (n+3) + (n+4))/5 = 18.
To solve this equation and find the value of n, we can simplify the equation:
(n + n + 1 + n + 2 + n + 3 + n + 4)/5 = 18.
Combining like terms, we get:
(5n + 10)/5 = 18.
Now, we can solve for n:
5n + 10 = 90.
Subtracting 10 from both sides, we have:
5n = 80.
Dividing both sides by 5, we get:
n = 16.
Therefore, the smallest number in the sequence is 16.