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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