The next term in the number series 10, 13, 22, 49, ______.
130
To find the next term in the series 10, 13, 22, 49, we need to observe the pattern followed by the numbers:
- The first term is 10.
- The difference between the second term and the first term is \(13 - 10 = 3\).
- The difference between the third term and the second term is \(22 - 13 = 9\).
- The difference between the fourth term and the third term is \(49 - 22 = 27\).
We notice that the differences follow a specific pattern:
- Differences: 3, 9, 27.
These differences are increasing in multiples of 3: \(3 \times 1, 3 \times 3, 3 \times 9\).
- The next difference should be \(3 \times 27 = 81\) because we're continuing the multiplication by 3 pattern.
Thus, the next term in the series will be:
\(49 + 81 = 130\)
This matches the pattern and the given correct option, making 130 the correct answer. Other options are incorrect as they do not follow the established pattern revealed by difference multiplication.
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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, ?
