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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Find the next term: 2, 6, 12, 20, 30, ?
40
42
44
46
42
Look at the differences between consecutive terms (+4, +6, +8, +10) which increase by 2 each time, meaning the next difference is +12.
Look at the differences between consecutive terms (+4, +6, +8, +10) which increase by 2 each time, meaning the next difference is +12.
Analyze Consecutive Differences
Find the difference between each adjacent pair: 6-2=4, 12-6=6, 20-12=8, and 30-20=10.
Identify the Pattern
The differences form an arithmetic progression increasing by 2 each time: 4, 6, 8, 10. The next logical difference is 12.
Calculate the Missing Term
Add the next difference to the last given term: 30 + 12 = 42.
A: 40 is incorrect as it results from adding only 10, C: 44 assumes an incorrect difference of 14, D: 46 overshoots the correct progression.
B is correct because the series follows the pattern n(n+1) for n=1 to 6, or an increasing difference pattern where 30 + 12 equals 42.
Always check the first and second level differences if a number series does not immediately fit standard squares, cubes, or multiplication rules.
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