Calculating the Sum of Consecutive Integers
_A_ is the sum of the consecutive integers from -5 to 5, inclusive.
| Quantity A | Quantity B |
|------------|------------|
|$$\frac{100}{(A+1)^2}$$ |$$\frac{100}{(A-1)^2}$$ |
Incorrect.
[[snippet]]
Make sure you calculate the sum correctly. Be careful with the negative signs when using the extremes to find the middle term and the number of terms.
Incorrect.
[[snippet]]
Ordinarily a number divided by a larger number will be smaller than that same number divided by a smaller number. The sum of the integers in this case, though, tells you something different about the relationship between the quantities.
Correct.
Start by calculating the sum of consecutive integers from -5 to 5, inclusive.
First, find the middle term by averaging the extremes.
$$\displaystyle (-5+5)\div 2=0\div 2=0$$
Next, add 1 to the difference of the extremes to find the number of terms.
$$\displaystyle 5-(-5)+1=5+5+1=11$$
Finally, multiply the middle term by the number of terms to find the sum.
$$\displaystyle 0\cdot 11=0$$
Quantity A is thus $$\frac{100}{(0+1)^2}=\frac{100}{1^2}=\frac{100}{1}=100$$.
Quantity B is $$\frac{100}{(0-1)^2}=\frac{100}{(-1)^2}=\frac{100}{1}=100$$.
The quantities are equal.
Incorrect.
[[snippet]]
There is enough information here to calculate the sum of the integers and compare the quantities.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
