What will come in place of question mark (?) in the following number series? 31, 32, 36, ?, 61, 86
45
Number Series Pattern Analysis: 31, 32, 36, ?, 61, 86
We need to find the missing number in the given series: 31, 32, 36, ?, 61, 86.
Let's examine the differences between consecutive terms to identify a pattern:
- Difference between the second and first term: $32 - 31 = 1$
- Difference between the third and second term: $36 - 32 = 4$
The differences observed are 1 and 4. We can recognize these numbers as perfect squares:
- $1 = 1^2$
- $4 = 2^2$
This suggests that the difference between consecutive terms might be increasing squares of consecutive integers.
Let's test this hypothesis:
- First term = 31
- Second term = First term + $1^2$ = $31 + 1 = 32$
- Third term = Second term + $2^2$ = $32 + 4 = 36$
- Missing term (Fourth term) = Third term + $3^2$ = $36 + 9 = 45$
Now, let's verify if this pattern holds for the remaining terms:
- Fifth term = Missing term + $4^2$ = $45 + 16 = 61$
- Sixth term = Fifth term + $5^2$ = $61 + 25 = 86$
The calculated terms match the given series (31, 32, 36, 45, 61, 86). Therefore, the pattern of adding consecutive squares ($1^2, 2^2, 3^2, 4^2, 5^2, ...$) is correct.
The missing number in the series is 45.
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 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?
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J12, M24, P48, S96, U192
In the following question, select the related number pair from the given alternatives.
144 : 400 :: ?
