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Refer to the series: 7, 10, 16, 28, 52, ? What is the next number in the series?
76
98
100
104
100
Observe the differences between consecutive terms; they follow a doubling pattern (3, 6, 12, 24, 48). Simply add the next power of 2 sequence to the last term.
Observe the differences between consecutive terms; they follow a doubling pattern (3, 6, 12, 24, 48). Simply add the next power of 2 sequence to the last term.
Analyze the differences between terms
Calculate the difference between consecutive numbers: 10-7=3, 16-10=6, 28-16=12, 52-28=24.
Identify the pattern
The differences (3, 6, 12, 24) are doubling each time. Therefore, the next difference must be 24 * 2 = 48.
Calculate the final term
Add the next difference (48) to the last term (52): 52 + 48 = 100.
A: 76 is incorrect as it results from adding 24 to 52; B: 98 is incorrect as it results from an arithmetic miscalculation; D: 104 is incorrect as it results from adding 52 instead of 48.
C is correct because the series follows a pattern where the difference between consecutive terms doubles (3, 6, 12, 24, 48), and 52 + 48 equals 100.
When a series grows rapidly, always check the difference of the differences; if the differences form a geometric progression, the original series involves exponential growth.
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