Question
upstudy study bank question image url

Select the number that will replace the questic
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:
  1. Position 1: 1
  2. Position 2: 9
  3. Position 3: 22
  4. Position 4: 32
  5. Position 5: 47
  6. Position 6: ?
  7. Position 7: 76
  8. Position 8: 90
  9. 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
  1. 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
  2. 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

error msg
Explain
Simplify this solution

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.

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy