The sum of 6 consecutive integers is 171. Find the smallest of the integers
From the problem statement, we know that some 6 integers must sum to 171. To get an idea of what these numbers are, start by dividing 171 by 6. This yields 28.5, which is what the average of our numbers are.
Here we can construct numbers close to this interval-- the problem did state these would be consecutive. Remember that we want the average to be 28.5, so start with 27, 28, 29. 30, 26, since they are the same distance from our current average 28 will preserve this average, so these are also numbers in the interval. We know that these numbers must sum to 171, so sum our current 5 numbers and subtract that from 171, yielding 31.
The numbers in question are therefore 26, 27, 28, 29, 30, 31. The smallest is 26.
or, using what you know about arithmetic progressions,
6/2 (2a+5*1) = 171
a = 26
so the numbers are as shown above.
13
To find the smallest of the six consecutive integers, we can set up an equation based on the given information. Let's denote the smallest integer as "x".
Since the six consecutive integers are consecutive, they would be x, x+1, x+2, x+3, x+4, and x+5.
The sum of these six consecutive integers is given as 171. So, we can set up the equation:
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) = 171
Now, we can solve this equation to find the value of x, which represents the smallest integer.
Combining like terms, we get:
6x + 15 = 171
Subtracting 15 from both sides of the equation:
6x = 171 - 15
6x = 156
Dividing both sides of the equation by 6:
x = 156 / 6
x = 26
Therefore, the smallest of the six consecutive integers is 26.