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.
Similar Questions
The missing term in the series 1, 4, 27, 16, ?, 36, 343, ... is
The next term in the series is .
56, 40, 27, 17, 10,
The next term in the number series 10, 13, 22, 49, ______.
The next term in the number series 41, 27, 16, 8, ______ is:
The next term in the series
0, 1, 9, 36, 100, ______ is:
In the sequence of numbers 1, 2, 6, 33, 49, 174, 210, x, ......., the term x is:
The next term in the series is:
2, 5, 9, 19, 37, ?
In the series 1, 6, 15, 28, 45, .......... the next term will be:
If the series 4, 5, 8, 13, 14, 17, 22, .... is continued in the same pattern, which one of the following is not a term of this series?
The next term in the series −1, 5, 15, 29, ?, ... is:
Important Questions from Number Series
- In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 676 :: 17 : Y - Which of the following options should come in place of the question mark (?) in the given series to make it logically complete?
125, 128, 133, 140, 149,? - What should come in place of the question mark (?) in the given series?
801 800 792 765 701 ? - What should come in place of the question mark (?) in the given series?
101 110 121 134 149 ? - What should come in place of the question mark (?) in the given series?
40, 48, 58, 66, 76, ?
