Question 25

In the sequence $$0, 7, 26, 63, 124, \ldots$$ the $$6^{\text{th}}$$ term is

Correct Answer: 215

Solution

Each term is one less than a perfect cube, since $$0 = 1^3 - 1$$, $$7 = 2^3 - 1$$, $$26 = 3^3 - 1$$, $$63 = 4^3 - 1$$ and $$124 = 5^3 - 1$$. So the $$n$$th term is $$n^3 - 1$$ and the sixth term is $$6^3 - 1 = 216 - 1 = 215$$.

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