The next number in the series 6, 12, 20, 30 is 42.
Understanding the Pattern
This number series follows a pattern where the difference between consecutive numbers increases by 2 each time. Let's break it down:
- 6
- 12 - 6 = 6
- 20 - 12 = 8
- 30 - 20 = 10
Notice the differences (6, 8, 10) form an arithmetic sequence with a common difference of 2. Following this pattern, the next difference would be 10 + 2 = 12. Therefore, the next number in the series is 30 + 12 = 42.
Multiple Sources Confirm the Answer
Several online sources, including Quora and other math forums (as referenced below) confirm this solution. Many examples show the continuation of the series as 6, 12, 20, 30, 42, 56, and so on.
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Quora: Multiple Quora threads (https://www.quora.com/What-is-the-next-number-in-the-sequence-6-12-20-30, https://mathprobssolutions.quora.com/What-is-the-next-number-in-the-given-series-0-2-6-12-20, https://www.quora.com/What-is-the-next-number-in-the-series-2-6-12-20-30, https://mathopedia.quora.com/What-is-the-next-number-in-the-series-2-6-12-20-30) clearly indicate 42 as the next number in similar series.
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Other Math Forums: Other online math communities (https://www.reddit.com/r/learnmath/comments/16lreoy/figure_the_next_unknown_in_the_pattern_4_6_12_20/, https://mathforums.com/t/next-number-in-the-series.10459/, https://testbook.com/question-answer/select-the-missing-number2-6-12-20-30--5f97b59057c890c1ed0da58c, https://www.sawaal.com/odd-man-out-and-series-questions-and-answers/insert-the-missing-number--2-6-12-20-30-42-56-_6467) also support this conclusion, although some show variations in the initial numbers of their sequences.
