In the following question, select the missing number from the given series. 5, 10, 17, 26, 37, ?, 65
50
Number Series Puzzle: Find the Missing Term
The question asks us to identify the missing number in the given number series: 5, 10, 17, 26, 37, ?, 65.
Analyzing the Number Series Pattern
Let's examine the differences between consecutive terms in the series to find the underlying pattern:
- Difference between the 2nd and 1st term: $10 - 5 = 5$
- Difference between the 3rd and 2nd term: $17 - 10 = 7$
- Difference between the 4th and 3rd term: $26 - 17 = 9$
- Difference between the 5th and 4th term: $37 - 26 = 11$
We can observe that the differences between consecutive terms are increasing by 2 each time (5, 7, 9, 11). This suggests an arithmetic progression in the differences.
Calculating the Missing Number
Following the pattern of differences, the next difference should be $11 + 2 = 13$. Therefore, the missing number is found by adding this difference to the previous term (37):
Missing Number = $37 + 13 = 50$
Let's verify this by checking the difference between the last term (65) and our calculated missing number (50). The difference should be $13 + 2 = 15$.
Check: $65 - 50 = 15$. The pattern holds true.
Alternative Pattern Verification
Another way to look at the series is by relating it to squares:
- $5 = 2^2 + 1 \quad (4 + 1)$
- $10 = 3^2 + 1 \quad (9 + 1)$
- $17 = 4^2 + 1 \quad (16 + 1)$
- $26 = 5^2 + 1 \quad (25 + 1)$
- $37 = 6^2 + 1 \quad (36 + 1)$
The pattern appears to be $n^2 + 1$, where 'n' starts from 2 and increases by 1 for each subsequent term.
Following this pattern, the missing term corresponds to $n=7$:
Missing Number = $7^2 + 1 = 49 + 1 = 50$
The next term (65) corresponds to $n=8$:
Next Term = $8^2 + 1 = 64 + 1 = 65$. This confirms the pattern.
Conclusion
Both methods confirm that the missing number in the series is 50. This corresponds to the first option provided.
Important Questions from Series
Select the option figure in which the given figure (X) is embedded (rotation is NOT allowed).
Identify the figure given in the options which when put in place of ? will logically complete the series.
When is a series of terms said to be in the order of increasing extension?
(A) When each term in the series (except the first) denotes a class having more members than a class denoted by the term preceding it.
(B) When the class size gets larger with each successive term.
(C) When each term in the series (except the first) denotes a class having fewer members than the class denoted by the term preceding it.
(D) When the class size gets smaller with each successive term
Choose the most appropriate answer from the options given below :
In the following question, select the missing number from the given series.
5, 10, 17, 26, 37, ?, 65
Identify the figure that best fits in place of the question mark.
