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Complete the series: 10, 15, 25, 45, 85, ?
165
155
175
145
165
Observe the differences between consecutive terms; they follow a geometric progression of powers of 2 (5, 10, 20, 40, 80).
Observe the differences between consecutive terms; they follow a geometric progression of powers of 2 (5, 10, 20, 40, 80).
Analyze the difference between terms
Calculate the difference between consecutive numbers: 15-10=5, 25-15=10, 45-25=20, 85-45=40.
Identify the pattern
The differences are 5, 10, 20, 40. Each difference is double the previous difference (52=10, 102=20, 20*2=40).
Calculate the next term
The next difference must be 40*2 = 80. Adding this to the last term: 85 + 80 = 165.
B: 155 is wrong because it corresponds to adding 70 instead of 80. C: 175 is wrong because it corresponds to adding 90. D: 145 is wrong because it corresponds to adding 60.
A is correct because the series follows a pattern of increasing differences by doubling the previous increment, resulting in 85 + 80 = 165.
When terms in a series grow at an accelerating rate, always check the difference between the differences (double-difference method).
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