Question 98

Choose the correct alternative to complete the following series.

1, 3, 7, 15, 31, ?

Solution

Each term is twice the previous term plus 1, as $$1 \times 2 + 1 = 3$$, $$3 \times 2 + 1 = 7$$ and so on. So the next term is $$31 \times 2 + 1 = 63$$. The terms are also $$2^n - 1$$.

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