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Find the missing term: 2, 5, 10, 17, 26, ?
35
37
39
41
37
Observe that the series follows the pattern n squared plus 1, where n is the position of the term starting from 1.
Observe that the series follows the pattern n squared plus 1, where n is the position of the term starting from 1.
Analyze the pattern
List the terms and their relationship to squares: 2 = 1┬▓ + 1, 5 = 2┬▓ + 1, 10 = 3┬▓ + 1, 17 = 4┬▓ + 1, 26 = 5┬▓ + 1.
Determine the next term
Following the sequence of n = 1, 2, 3, 4, 5, the next term must be 6┬▓ + 1. Calculating 36 + 1 results in 37.
Alternative common difference check
Calculate the differences between consecutive terms: 5-2=3, 10-5=5, 17-10=7, 26-17=9. The differences are consecutive odd numbers. The next difference should be 11. Thus, 26 + 11 = 37.
A: 35 is incorrect because the difference from 26 is only 9, whereas the series requires an increment of 11. C: 39 is incorrect because 6 squared plus 3 does not follow the consistent plus 1 rule. D: 41 is incorrect because it corresponds to 6 squared plus 5, deviating from the established plus 1 logic.
B is correct because the series follows the formula n squared plus 1 for n=1 to 6, leading to 6 squared plus 1 equals 37.
If differences between numbers are increasing by 2 (3, 5, 7, 9, 11), always check if the terms relate to squares of integers to verify your logic quickly.
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