Question
Select the number that will replace the questic
mark (?) in the given series.
mark (?) in the given series.
Ask by Whittaker Wells. in India
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The missing number is 59.
Solution
To determine the missing number in the series:
Step 1: Analyze the Series
Let’s list the terms with their positions:
- Position 1: 1
- Position 2: 9
- Position 3: 22
- Position 4: 32
- Position 5: 47
- Position 6: ?
- Position 7: 76
- Position 8: 90
- Position 9: 109
Step 2: Separate Odd and Even Positions
- Odd Positions (1, 3, 5, 7, 9): 1, 22, 47, 76, 109
- Even Positions (2, 4, 6, 8): 9, 32, ?, 90
Step 3: Identify Patterns Separately
-
Odd Positions:
- Differences:
- 1 to 22: +21
- 22 to 47: +25
- 47 to 76: +29
- 76 to 109: +33
- Pattern: Each difference increases by 4.
- 21, 21 + 4 = 25, 25 + 4 = 29, 29 + 4 = 33
- Differences:
-
Even Positions:
-
Known Terms: 9, 32, ?, 90
-
Differences:
- 9 to 32: +23
- 32 to ?: ?
- ? to 90: ?
-
Assumed Pattern: Similar to odd positions, increase each difference by 4.
- First difference: +23
- Next difference: 23 + 4 = 27
- Following difference: 27 + 4 = 31
-
Calculations:
- 32 + 27 = 59
- 59 + 31 = 90 (which matches the given series)
-
Step 4: Conclusion
The missing number at Position 6 is 59.
Complete Series:
Answer: 59
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
To find the number that will replace the question mark (?), let’s examine the differences between consecutive numbers in the series.
Starting with the given series:
Calculating the differences:
The differences so far:
If we analyze the differences pattern, we can see that the differences seem to be alternating or following a particular addition pattern:
Notice how:
- 8 (1+7)
- 13 (5+8)
- 10 (4+6)
- 15 (5+10)
- The difference to go from 47 to the next number can likely center around 29, which fits the difference between 76 and the unknown number (29 or so).
If we calculate this, we have:
- 47 + 29 = 76 (assumed the pattern continues smoothly).
Thus, the missing number after 47 is:
To confirm:
- Results show that moving from 47 to 76 takes a difference of 29 indeed.
Thus, the number that will replace the question mark (?) is 62.