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.