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Identify the missing number: 7, 10, 16, 28, 52, ?
84
96
100
104
100
Notice that the differences between consecutive terms double each time (+3, +6, +12, +24, +48), allowing you to quickly find the next term.
Notice that the differences between consecutive terms double each time (+3, +6, +12, +24, +48), allowing you to quickly find the next term.
Find Differences
Calculate the difference between consecutive terms: 10 - 7 = 3, 16 - 10 = 6, 28 - 16 = 12, and 52 - 28 = 24.
Identify Pattern
The sequence of differences is 3, 6, 12, 24, where each difference is multiplied by 2. Thus, the next difference is 24 * 2 = 48.
Calculate Missing Term
Add the next difference to the final given term: 52 + 48 = 100.
A: 84 is incorrect because it results from faulty arithmetic; B: 96 is incorrect as it assumes a difference of 44 instead of 48; D: 104 is incorrect because it assumes a difference of 52.
C is correct because the differences between consecutive terms double successively (+3, +6, +12, +24), making the next difference 48 and yielding 52 + 48 = 100.
When consecutive differences grow rapidly, always check whether the differences themselves form an arithmetic or geometric progression.
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