1. The problem states a sequence defined by the recurrence relation $$a_n = 2a_{n-1} + 1$$ with the initial term $$a_1 = 1$$. We need to find the 5th term, $$a_5$$. 2. The recurrence relation means each term is twice the previous term plus 1. 3. Let's calculate the terms step-by-step: - $$a_1 = 1$$ (given) - $$a_2 = 2a_1 + 1 = 2 \times 1 + 1 = 3$$ - $$a_3 = 2a_2 + 1 = 2 \times 3 + 1 = 7$$ - $$a_4 = 2a_3 + 1 = 2 \times 7 + 1 = 15$$ - $$a_5 = 2a_4 + 1 = 2 \times 15 + 1 = 31$$ 4. Therefore, the 5th term of the sequence is $$31$$. 5. The answer corresponds to option C) 31.