Solving the Number Series: 0, 7, 26, 63, ?

The question asks to find the next term in the given number series: 0, 7, 26, 63.

Identifying the Series Pattern

Let's examine the relationship between the terms and their position in the series. We can observe a pattern related to the cubes of consecutive integers:

• The first term is 0. This can be represented as $1^3 - 1 = 1 - 1 = 0$.
• The second term is 7. This can be represented as $2^3 - 1 = 8 - 1 = 7$.
• The third term is 26. This can be represented as $3^3 - 1 = 27 - 1 = 26$.
• The fourth term is 63. This can be represented as $4^3 - 1 = 64 - 1 = 63$.

The pattern identified is that each term is one less than the cube of its position number ($n^3 - 1$, starting with $n=1$).

Calculating the Next Term

To find the next term in the series, we need to apply the same pattern for the fifth position ($n=5$):

• The fifth term = $5^3 - 1$
• $5^3 = 5 \times 5 \times 5 = 125$
• Fifth term = $125 - 1 = 124$

Conclusion

The missing term in the series 0, 7, 26, 63 is 124.