76, 80, 71, 87, 62, ?
Number Series Analysis
The given number series is: 76, 80, 71, 87, 62, ?
Identifying the Pattern
We observe the difference between consecutive terms:
- $80 - 76 = +4$
- $71 - 80 = -9$
- $87 - 71 = +16$
- $62 - 87 = -25$
The operations involve adding and subtracting perfect squares:
- $+4$ is $+2^2$
- $-9$ is $-3^2$
- $+16$ is $+4^2$
- $-25$ is $-5^2$
The pattern is an alternating addition and subtraction of squares of consecutive integers ($2^2, 3^2, 4^2, 5^2, ...$).
Calculating the Next Term
To find the number that replaces the question mark, we continue the pattern. The last operation was subtraction ($-5^2$), so the next operation is addition ($+6^2$).
The calculation is: $62 + 6^2$
Calculate the value: $62 + 36 = 98$
Conclusion
The number that should come in place of the question mark '?' is 98.
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Important Questions from Number Series
Select the number from among the given options that can replace the question mark (?) in the following series.
37, 52, 74, 104, 143, ?
Select the number that can replace the question mark (?) in the following series.
17, 19, 22, 27, 34, 45, 58,?Select the number from among the given options that can replace the question mark (?) in the following series.
10, 14, 31, 35, 73, 77, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
215, 231, 256, 292, ?
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 6, 8, 24, 28, 140, ?
