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What should come in place of the question mark (?) in the given series? 49 65 97 145 209 ?
279
294
289
284 Question ID : 4410091983890 Option 1 ID : 4410097814127 Option 2 ID : 4410097814126 Option 3 ID : 4410097814125 Option 4 ID : 4410097814128 Status : Answered Chosen Option : C
289
Calculate the difference between consecutive terms; the differences form a series of square numbers multiplied by 4 (44, 49, 416, 425, 4*36).
Calculate the difference between consecutive terms; the differences form a series of square numbers multiplied by 4 (44, 49, 416, 425, 4*36).
Analyze the difference between terms
Find the difference between consecutive numbers: 65-49 = 16, 97-65 = 32, 145-97 = 48, 209-145 = 64.
Identify the pattern in differences
The differences are 16, 32, 48, 64. These are multiples of 16 (16x1, 16x2, 16x3, 16x4). The next difference must be 16x5 = 80.
Calculate the final term
Add the next difference to the last known term: 209 + 80 = 289.
A: 279 is incorrect as it results from adding 70 instead of 80; B: 294 is mathematically inconsistent with the established difference pattern; D: 284 is incorrect because it implies a difference of 75 instead of 80.
C is correct because the series follows a pattern of adding successive multiples of 16 (16, 32, 48, 64, 80) to each preceding term, leading to 209 + 80 = 289.
When terms in a series grow at an accelerating rate, always check the difference of the differences (second-order difference) to reveal hidden multiplication patterns.
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