Sequences: Consecutive Integers - Calculating the Sum of Consecutive Integers

The sum of the consecutive odd integers from -21 to 31, inclusive, is

Correct. The sum of the consecutive odd integers from -21 to 21 is 0 because each negative value cancels out its positive counterpart. Based on this, add odd integers from 23 to 31 to get the sum of consecutive integers from -21 to 31. >$$\text{Sum} = 23 + 25 + 27 + 29 + 31 = 135$$ Hence, this is the correct answer.

Incorrect. [[Snippet]]

Incorrect. [[Snippet]]

Incorrect. [[Snippet]]

Incorrect. [[Snippet]] Did you fail to notice that the question asked about consecutive odd integers? Don't be hasty—read the question carefully.

Sure. According to the formula, we require both the average of the set and the number of terms in the set to calculate its sum: >$$\text{Sum of terms} = \text{Average of terms} \times \text{Number of terms}$$ The number of terms is calculated by subtracting the smallest term from the greatest term, dividing by 2 (since it's a sequence of odd integers), and then adding one: >$$\text{Difference} = 31-(-21) = 52$$ >$$\text{Number of terms} = \frac{52}{2} + 1 = 27$$ As for the set's average, average the __first__ and __last terms__ to find the "middle" of the set: >$$\text{Average} = \frac{-21 + 31}{2} = \frac{10}{2} = 5$$. __Plug In__ the sum and the number of terms into the formula: >$$\text{Sum of terms} = 5\times 27 = 135$$.

Okay. Let's move on.

130

135

150

156

235

Got it!

Can this problem be solved using the __sum of terms__ formula?