Complete the series. 2, 6, 12, 20, 30, 42, 56, (…)
Correct Answer:
D. 72
Explanation:
To find the next number in the sequence 2, 6, 12, 20, 30, 42, 56, (...), we can examine the pattern of differences between consecutive terms: - 6 - 2 = 4 - 12 - 6 = 6 - 20 - 12 = 8 - 30 - 20 = 10 - 42 - 30 = 12 - 56 - 42 = 14The differences follow a pattern of increasing by 2 each time (4, 6, 8, 10, 12, 14). To find the next term, we add 16 (the next even number after 14) to the last term: 56 + 16 = 72. Alternatively, the series follows the formula n(n+1) for n = 1, 2, 3... (1x2=2, 2x3=6, 3x4=12, 4x5=20, 5x6=30, 6x7=42, 7x8=56). The next term is 8x9 = 72.
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