Select the number from among the given options that can replace the question mark (?) in the following series. 5, 18, 39, 68, 105, ?
Number Series Pattern Analysis
To find the number that replaces the question mark (?) in the series 5, 18, 39, 68, 105, ?, we need to identify the pattern.
Analyzing First Differences
First, calculate the difference between consecutive terms in the series:
- Difference between 18 and 5: $18 - 5 = 13$
- Difference between 39 and 18: $39 - 18 = 21$
- Difference between 68 and 39: $68 - 39 = 29$
- Difference between 105 and 68: $105 - 68 = 37$
The sequence of first differences is 13, 21, 29, 37.
Identifying Second Differences
Next, find the difference between consecutive terms in the first difference sequence (the second differences):
- Difference between 21 and 13: $21 - 13 = 8$
- Difference between 29 and 21: $29 - 21 = 8$
- Difference between 37 and 29: $37 - 29 = 8$
The second difference is constant and equals 8. This confirms a consistent pattern.
Calculating the Next Term
To find the next first difference, add the constant second difference (8) to the last calculated first difference (37):
$37 + 8 = 45$
This means the difference between the last term (105) and the missing term (?) is 45.
Finally, add this next difference (45) to the last term of the series (105) to find the missing number:
$105 + 45 = 150$
Result
The number that replaces the question mark (?) in the series is 150.
Similar Questions
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Important Questions from Number Series
What will come in place of question mark (?) in the following number series?
2, 5, 11, 23, 44, 77, ?
What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86
What will come in the place of question mark (?) in the following number series?
3, 6, 18, ?, 630, 6930
What should come in place of the question mark ‘?’ in the following number series?
60, 40, 50, ?, 180, 460
A series is given with one term wrong. Select that wrong term from the given alternatives.
J12, M24, P48, S96, U192
