The next term in the series is: 2, 5, 9, 19, 37, ?
75
A number series is solved by finding a single rule that carries each term to the next, so the first step is to see how consecutive terms are related.
The differences are 3, 4, 10, 18, which form no obvious pattern, so a purely additive rule can be set aside. Looking instead at ratios, each term is roughly double the previous one, which suggests a multiplicative rule with a small correction.
Testing that idea: 2 × 2 + 1 = 5; 5 × 2 − 1 = 9; 9 × 2 + 1 = 19; 19 × 2 − 1 = 37. The rule holds throughout - each term is doubled, and one is alternately added and subtracted.
Since the last operation applied was a subtraction, the next must be an addition: 37 × 2 + 1 = 75.
The distractors are placed to catch partial reasoning. Choosing 73 comes from applying the wrong sign, 37 × 2 − 1, and so from missing the alternation. The values 78 and 80 do not follow from any consistent doubling rule at all.
Hence the next term in the series is 75.
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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, ?
