{"status": "success", "data": {"description_md": "Munch has a $3\\times3$ grid with the following rules:\n\n**1.** The first and second rows from the top form an arithmetic series\n**2.** Every column forms a geometric series.\n**3.** The main diagonal from top left to bottom right is both an arithmetic and geometric series.\n\nAn arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant (the common difference) to the previous term. For example, $4, 7, 10, 13, 16$ is an arithmetic sequence with $5$ terms and a common difference of $3$.\n\nA geometric sequence is a sequence of numbers such that the ratio between any two consecutive terms is constant. This constant is called the common ratio of the sequence. For example, $1, 2, 4, 8$ is a geometric sequence with $4$ terms and a common ratio of $2$.\n\nSeveral of the cells are already filled, as shown. What is the sum of the values of every cell?\n\n<img src=\"/static/p1.17.png\" width=\"200px\"><br>\n\n$(\\textbf{A})\\;32\\quad(\\textbf{B})\\;35\\quad(\\textbf{C})\\;33\\quad(\\textbf{D})\\;34\\quad(\\textbf{E})\\;38$", "description_html": "<p>Munch has a <span class=\"katex--inline\">3\\times3</span> grid with the following rules:</p>&#10;<p><strong>1.</strong> The first and second rows from the top form an arithmetic series<br/>&#10;<strong>2.</strong> Every column forms a geometric series.<br/>&#10;<strong>3.</strong> The main diagonal from top left to bottom right is both an arithmetic and geometric series.</p>&#10;<p>An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant (the common difference) to the previous term. For example, <span class=\"katex--inline\">4, 7, 10, 13, 16</span> is an arithmetic sequence with <span class=\"katex--inline\">5</span> terms and a common difference of <span class=\"katex--inline\">3</span>.</p>&#10;<p>A geometric sequence is a sequence of numbers such that the ratio between any two consecutive terms is constant. This constant is called the common ratio of the sequence. For example, <span class=\"katex--inline\">1, 2, 4, 8</span> is a geometric sequence with <span class=\"katex--inline\">4</span> terms and a common ratio of <span class=\"katex--inline\">2</span>.</p>&#10;<p>Several of the cells are already filled, as shown. What is the sum of the values of every cell?</p>&#10;<p><img src=\"/static/p1.17.png\" width=\"200px\"/><br/></p>&#10;<p><span class=\"katex--inline\">(\\textbf{A})\\;32\\quad(\\textbf{B})\\;35\\quad(\\textbf{C})\\;33\\quad(\\textbf{D})\\;34\\quad(\\textbf{E})\\;38</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "Mock AMC 8 #1 - Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/amc8mock1-p18", "prev": "/problem/amc8mock1-p16"}}