GMAT Practice Question: What is the sum of the odd integers from 35 to 85, inclusive?
Question
What is the sum of the odd integers from 35 to 85, inclusive?
- 1,560
- 1,500
- 1,240
- 1,120
- 1,100
Topics: odds/evens, sequences & series, sums of integers
Solution
Step 1
We first note the key features of our sequence: the first term, the last term, and the constant gap (step) between consecutive odd numbers.
a_1 = 35 a_{n} = 85 \text{step} = 2
Step 2
Next, we count how many terms appear in this evenly spaced list. By the \textbf{\text{"Counting Evenly Spaced Integers"}} rule, we subtract the endpoints, divide by the step, and add one because the list is inclusive.
n = \frac{85 - 35}{2} + 1 = \frac{50}{2} + 1 = 25 + 1 = 26
Step 3
For an evenly spaced list, the average value equals the mean of the first and last terms.
\text{average} = \frac{35 + 85}{2} = \frac{120}{2} = 60
Step 4
Finally, we apply the \textbf{\text{"Sum of Evenly Spaced Integers"}} rule: the sum equals the average multiplied by the number of terms.
\text{sum} = 60 \times 26 = (60 \times 20) + (60 \times 6) = 1200 + 360 = 1560
Answer
The sum of the odd integers from 35 to 85 inclusive is 1,560.
