{"status": "success", "data": {"description_md": "A four-term sequence is formed by adding each term of a four-term arithmetic sequence of positive integers to the corresponding term of a four-term geometric sequence of positive integers. The first three terms of the resulting four-term sequence are $57$, $60$, and $91$. What is the fourth term of this sequence? \n\n$\\textbf{(A) } 190 \\qquad \\textbf{(B) } 194 \\qquad \\textbf{(C) } 198 \\qquad \\textbf{(D) } 202 \\qquad \\textbf{(E) } 206$", "description_html": "<p>A four-term sequence is formed by adding each term of a four-term arithmetic sequence of positive integers to the corresponding term of a four-term geometric sequence of positive integers. The first three terms of the resulting four-term sequence are  <span class=\"katex--inline\">57</span> ,  <span class=\"katex--inline\">60</span> , and  <span class=\"katex--inline\">91</span> . What is the fourth term of this sequence?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 190 \\qquad \\textbf{(B) } 194 \\qquad \\textbf{(C) } 198 \\qquad \\textbf{(D) } 202 \\qquad \\textbf{(E) } 206</span> </p>\n<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": "2022 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc10A_p21", "prev": "/problem/22_amc10A_p19"}}