College Math Placement Practice Test

What is the next term in the sequence 2, 5, 10, 17?

1. 20

2. 21

3. 25

4. 26

The correct answer is: 26

To determine the next term in the sequence 2, 5, 10, 17, we can start by looking at the differences between consecutive terms. - The difference between 5 and 2 is 3. - The difference between 10 and 5 is 5. - The difference between 17 and 10 is 7. So far, our differences are 3, 5, and 7. If we observe these differences, we can see that they form their own sequence: 3, 5, 7, which increases by 2 each time. Continuing this pattern, the next difference would be 9 (7 + 2). Now, we add this next difference to the last term of the original sequence: 17 (the last term) + 9 (the next calculated difference) equals 26. Thus, the next term in the sequence is 26.