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What is the next number in the sequence: 4, 9, 19, 39, 79, ?
159
157
161
155
159
Multiply each term by 2 and add 1 (e.g., 4x2+1=9, 9x2+1=19), or notice that the differences between consecutive terms double each time.
Multiply each term by 2 and add 1 (e.g., 4x2+1=9, 9x2+1=19), or notice that the differences between consecutive terms double each time.
Step 1: Calculate consecutive differences
Find the difference between each adjacent pair: 9 - 4 = 5, 19 - 9 = 10, 39 - 19 = 20, and 79 - 39 = 40.
Step 2: Identify the pattern in differences
The differences are 5, 10, 20, 40, which double at each step. Therefore, the next difference must be 80.
Step 3: Compute the final term
Add the next difference to the last term of the series: 79 + 80 = 159.
B: 157 is incorrect because it results from adding 78 instead of 80. C: 161 is incorrect because it results from adding 82 instead of 80. D: 155 is incorrect because it results from adding 76 instead of 80.
A is correct because the sequence follows a doubling difference pattern (5, 10, 20, 40, 80), and adding 80 to 79 gives 159.
If the differences between terms grow rapidly, test for a multiplicative relation combined with addition or subtraction, such as multiplying by 2 and adding a constant.
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