512 513 505 532 468 ?
The question asks to find the missing number in the series: 512, 513, 505, 532, 468, ?
Series Pattern Identification
Let's examine the differences between consecutive terms in the series:
- $513 - 512 = +1$
- $505 - 513 = -8$
- $532 - 505 = +27$
- $468 - 532 = -64$
The differences are $1, -8, 27, -64$. We can recognize these numbers as perfect cubes:
- $1 = 1^3$
- $-8 = (-2)^3$
- $27 = 3^3$
- $-64 = (-4)^3$
The pattern involves adding and subtracting cubes of consecutive integers starting from 1. The sequence of operations is: +$1^3$, -$2^3$, +$3^3$, -$4^3$.
Calculating the Missing Term
Following the established pattern, the next operation should be adding the cube of 5, which is $5^3$.
- The next term in the series is $468 + 5^3$.
- Calculate $5^3$: $5 \times 5 \times 5 = 125$.
- Add this to the last term: $468 + 125 = 593$.
Therefore, the number that should come in place of the question mark (?) is 593.
Similar Questions
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Important Questions from Number Series
What will come in place of question mark (?) in the following number series?
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What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86
What will come in the place of question mark (?) in the following number series?
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A series is given with one term wrong. Select that wrong term from the given alternatives.
J12, M24, P48, S96, U192
