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Which of the following options should come in place of the question mark (?) in the given series? 7, 15, 24, 34, 45,?
60
55
57
58
57
Look at the differences between consecutive terms: 15-7=8, 24-15=9, 34-24=10, 45-34=11. The differences are increasing by 1 each time (+8, +9, +10, +11). The next difference is +12.
Look at the differences between consecutive terms: 15-7=8, 24-15=9, 34-24=10, 45-34=11. The differences are increasing by 1 each time (+8, +9, +10, +11). The next difference is +12.
Analyze consecutive differences
Find the difference between each adjacent pair in the series: 15 minus 7 is 8, 24 minus 15 is 9, 34 minus 24 is 10, and 45 minus 34 is 11.
Identify the pattern
The differences form an arithmetic progression increasing by 1 each time: +8, +9, +10, +11.
Calculate the missing number
Following the pattern, the next difference must be +12. Adding 12 to the last term gives 45 + 12 = 57.
A: 60 is incorrect because adding 15 would be required, not 12. B: 55 is incorrect because it corresponds to adding 10 twice instead of 11 and 12. D: 58 is incorrect because it assumes a difference of +13.
C is correct because the series follows a pattern of increasing differences (+8, +9, +10, +11, +12), making the next term 45 + 12 = 57.
Always check both single-difference and double-difference (difference of differences) when the first-level differences change at a constant rate.
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