{"status": "success", "data": {"description_md": "Jacob uses the following procedure to write down a sequence of numbers. First he chooses the first term to be $6$. To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts $1$. If it comes up tails, he takes half of the previous term and subtracts $1$. What is the probability that the fourth term in Jacob's sequence is an integer?\n\n$\\mathrm{(A)}\\ \\frac{1}{6}\\qquad\\mathrm{(B)}\\ \\frac{1}{3}\\qquad\\mathrm{(C)}\\ \\frac{1}{2}\\qquad\\mathrm{(D)}\\ \\frac{5}{8}\\qquad\\mathrm{(E)}\\ \\frac{3}{4}$", "description_html": "<p>Jacob uses the following procedure to write down a sequence of numbers. First he chooses the first term to be <span class=\"katex--inline\">6</span>. To generate each succeeding term, he flips a fair coin. If it comes up heads, he doubles the previous term and subtracts <span class=\"katex--inline\">1</span>. If it comes up tails, he takes half of the previous term and subtracts <span class=\"katex--inline\">1</span>. What is the probability that the fourth term in Jacob&#8217;s sequence is an integer?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac{1}{6}\\qquad\\mathrm{(B)}\\ \\frac{1}{3}\\qquad\\mathrm{(C)}\\ \\frac{1}{2}\\qquad\\mathrm{(D)}\\ \\frac{5}{8}\\qquad\\mathrm{(E)}\\ \\frac{3}{4}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2008 AMC 10A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc10A_p23", "prev": "/problem/08_amc10A_p21"}}