The next number in the sequence 2, 5, 10, 17 is 26. The pattern follows the addition of consecutive odd numbers:
- 2 + 3 = 5
- 5 + 5 = 10
- 10 + 7 = 17
- 17 + 9 = 26
This pattern continues by adding the next consecutive odd number (11) to 26, resulting in 37, and then adding 13 to get 50, and finally adding 15 to get 65. Therefore, the next three terms in the sequence are 37, 50, and 65.
Multiple sources confirm this pattern and solution:
- Cuemath: https://www.cuemath.com/questions/how-do-you-find-the-next-three-terms-in-2-5-10-17-26/ explicitly states that the next three terms are 37, 50, and 65.
- Quora: Several Quora threads (https://www.quora.com/What-is-the-rule-of-sequence-in-2-5-10-and-17, https://mathresources.quora.com/Which-number-should-come-next-in-the-sequence-2-5-10-17-and-26, https://www.quora.com/What-comes-next-in-this-sequence-1-2-5-10-17-26, https://mathprobssolutions.quora.com/What-is-next-in-this-sequence-2-5-10-17-26-37) also support the same conclusion.
- Socratic: https://socratic.org/questions/how-do-you-find-the-next-three-terms-in-2-5-10-17-26 and https://socratic.org/questions/how-do-you-find-the-nth-term-of-the-sequence-2-5-10-17-26-37 discuss the sequence and its pattern.
- Mathway and Chegg: These sites (https://www.mathway.com/popular-problems/Algebra/793708, https://www.chegg.com/homework-help/questions-and-answers/10119-find-formula-nth-term-sequence-2-5-10-17-26--determine-sequence-s-formula-terms-n-n2-q30051525) further solidify the solution by analyzing the differences between consecutive terms.
- Toppr: https://www.toppr.com/ask/question/find-the-next-term-of-the-sequence-2-5-10-17-26/ also provides the correct next term in the sequence.
The sequence can also be expressed as a quadratic equation: n² + 1, where n represents the position of the number in the sequence.
