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Select the number from among the given options that can replace the question mark (?) in the following series: 45, 95, 245, 695,?
2045
1995
2125
2075
2045
Analyze the successive differences or multipliers. Here, each term is multiplied by an increasing number and added/subtracted, or check the pattern of differences: 50, 150, 450, 1350...
Analyze the successive differences or multipliers. Here, each term is multiplied by an increasing number and added/subtracted, or check the pattern of differences: 50, 150, 450, 1350...
Step 1: Find the difference between consecutive terms
Calculate the difference between each adjacent pair: 95 - 45 = 50, 245 - 95 = 150, 695 - 245 = 450.
Step 2: Identify the pattern among differences
The differences are 50, 150, 450. Each difference is multiplied by 3 to get the next difference (50 x 3 = 150, 150 x 3 = 450).
Step 3: Calculate the next difference
The next difference in the sequence will be 450 x 3 = 1350.
Step 4: Find the missing number
Add the calculated difference to the last term: 695 + 1350 = 2045.
B: 1995 is incorrect as it results from a wrong difference increment. C: 2125 is incorrect due to arithmetic error in multiplying differences. D: 2075 is incorrect and does not match the geometric progression of differences.
A is correct because the series follows a pattern where the differences between consecutive terms form a geometric progression multiplied by 3 (50, 150, 450, 1350), yielding 695 + 1350 = 2045.
When differences between terms grow rapidly in a non-linear fashion, always check for multiplication patterns within the differences or alternating double-difference methods.
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