The next term in the series 2, 5, 10, 17, 26, 37, ? is:
50
The standard first step with a number series is to take the differences between consecutive terms, because a pattern that is hidden in the terms themselves is often obvious in the gaps.
The differences are 5 - 2 = 3, 10 - 5 = 5, 17 - 10 = 7, 26 - 17 = 9 and 37 - 26 = 11. These are the consecutive odd numbers 3, 5, 7, 9, 11, so the next difference must be 13. Adding gives 37 + 13 = 50.
The same series can be seen a second way, which is a useful check. Each term is one more than a perfect square: 2 = 1 + 1, 5 = 4 + 1, 10 = 9 + 1, 17 = 16 + 1, 26 = 25 + 1, 37 = 36 + 1. The general term is therefore n squared plus 1, and for n = 7 this gives 49 + 1 = 50. Both methods agree, which confirms the answer.
The distractor 57 arises from wrongly continuing the differences as 3, 5, 7, 9, 11, 20 or from adding 20; 62 comes from assuming the differences double; and 72 is roughly twice 37, which fits no pattern in the series at all.
Hence the next term is 50.
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Important Questions from Number Series
What will come in place of question mark (?) in the following number series?
2, 5, 11, 23, 44, 77, ?
What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86
What will come in the place of question mark (?) in the following number series?
3, 6, 18, ?, 630, 6930
What should come in place of the question mark ‘?’ in the following number series?
60, 40, 50, ?, 180, 460
A series is given with one term wrong. Select that wrong term from the given alternatives.
J12, M24, P48, S96, U192
