{"status": "success", "data": {"description_md": "The geometric series $a+ar+ar^2\\cdots$ has a sum of $7$, and the terms involving odd powers of $r$ have a sum of $3$. What is $a+r$?\n\n$\\mathrm {(A)} \\frac{4}{3}\\qquad \\mathrm {(B)} \\frac{12}{7}\\qquad \\mathrm {(C)} \\frac{3}{2}\\qquad \\mathrm {(D)} \\frac{7}{3}\\qquad \\mathrm {(E)} \\frac{5}{2}$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The geometric series  <span class=\"katex--inline\">a+ar+ar^2\\cdots</span>  has a sum of  <span class=\"katex--inline\">7</span> , and the terms involving odd powers of  <span class=\"katex--inline\">r</span>  have a sum of  <span class=\"katex--inline\">3</span> . What is  <span class=\"katex--inline\">a+r</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm {(A)} \\frac{4}{3}\\qquad \\mathrm {(B)} \\frac{12}{7}\\qquad \\mathrm {(C)} \\frac{3}{2}\\qquad \\mathrm {(D)} \\frac{7}{3}\\qquad \\mathrm {(E)} \\frac{5}{2}</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2007 AMC 12B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12B_p16", "prev": "/problem/07_amc12B_p14"}}