3, 7, 14, 24, 37, ?
Sequence Pattern Identification
The problem requires finding the next number in the given sequence: 3, 7, 14, 24, 37, ?.
Analyzing Consecutive Differences
First, let's find the difference between each consecutive pair of numbers in the sequence:
- $7 - 3 = 4$
- $14 - 7 = 7$
- $24 - 14 = 10$
- $37 - 24 = 13$
Identifying the Difference Pattern
Observe the sequence of differences obtained: 4, 7, 10, 13. This sequence of differences forms an arithmetic progression. The difference between consecutive terms in this new sequence is constant:
- $7 - 4 = 3$
- $10 - 7 = 3$
- $13 - 10 = 3$
The common difference is 3.
Calculating the Next Term
To find the next number in the original sequence, we first need to determine the next difference in the sequence of differences. Following the pattern, the next difference will be:
- $13 + 3 = 16$
Now, add this next difference (16) to the last term of the original sequence (37) to find the missing number:
- $37 + 16 = 53$
Therefore, the number that should come at the place of the question mark is 53.
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Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
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Select the number that can replace the question mark (?) in the following series.
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Select the number from among the given options that can replace the question mark (?) in the following series.
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