{"generator":"equations.sequence","version":1,"value":{"problems":[{"prompt":"9, 2, 11, 13, 24, \u2026","prompt_latex":"9,\\; 2,\\; 11,\\; 13,\\; 24,\\; \\ldots","answer":"37   (each term is the sum of the two before it)","answer_latex":"37","kind":"fibonacci","rule":"each term is the sum of the two before it","terms":[9,2,11,13,24],"next":37},{"prompt":"1, -4, -11, -20, -31, \u2026","prompt_latex":"1,\\; -4,\\; -11,\\; -20,\\; -31,\\; \\ldots","answer":"-44   (quadratic, second difference -2)","answer_latex":"-44","kind":"quadratic","rule":"quadratic, second difference -2","terms":[1,-4,-11,-20,-31],"next":-44},{"prompt":"6, 18, 54, 162, 486, \u2026","prompt_latex":"6,\\; 18,\\; 54,\\; 162,\\; 486,\\; \\ldots","answer":"1458   (geometric, ratio 3)","answer_latex":"1458","kind":"geometric","rule":"geometric, ratio 3","terms":[6,18,54,162,486],"next":1458},{"prompt":"4, -8, 16, -32, 64, \u2026","prompt_latex":"4,\\; -8,\\; 16,\\; -32,\\; 64,\\; \\ldots","answer":"-128   (geometric, ratio -2)","answer_latex":"-128","kind":"geometric","rule":"geometric, ratio -2","terms":[4,-8,16,-32,64],"next":-128},{"prompt":"2, 2, 4, 6, 10, \u2026","prompt_latex":"2,\\; 2,\\; 4,\\; 6,\\; 10,\\; \\ldots","answer":"16   (each term is the sum of the two before it)","answer_latex":"16","kind":"fibonacci","rule":"each term is the sum of the two before it","terms":[2,2,4,6,10],"next":16}],"count":5},"display":"1. 9, 2, 11, 13, 24, \u2026   \u2192   37   (each term is the sum of the two before it)\n2. 1, -4, -11, -20, -31, \u2026   \u2192   -44   (quadratic, second difference -2)\n3. 6, 18, 54, 162, 486, \u2026   \u2192   1458   (geometric, ratio 3)\n4. 4, -8, 16, -32, 64, \u2026   \u2192   -128   (geometric, ratio -2)\n5. 2, 2, 4, 6, 10, \u2026   \u2192   16   (each term is the sum of the two before it)","meta":{"latex":[["9,\\; 2,\\; 11,\\; 13,\\; 24,\\; \\ldots","37"],["1,\\; -4,\\; -11,\\; -20,\\; -31,\\; \\ldots","-44"],["6,\\; 18,\\; 54,\\; 162,\\; 486,\\; \\ldots","1458"],["4,\\; -8,\\; 16,\\; -32,\\; 64,\\; \\ldots","-128"],["2,\\; 2,\\; 4,\\; 6,\\; 10,\\; \\ldots","16"]],"problems":5,"stream_bytes_used":20,"rejections":4,"entropy_in_bytes":16,"duration_us":301},"receipt":{"source":"random-org","source_label":"RANDOM.ORG","class":"A","class_label":"Cryptographic","caveat":null,"narrative":"Atmospheric radio noise, sampled in Dublin moments ago.","proof_url":"https:\/\/www.random.org\/randomness\/","reference":null,"observed_at":"2026-10-28T23:06:02+00:00","degraded":false,"mixed_with_csprng":true,"latency_ms":318,"cached":false},"seed":{"token":"YFSX4MXTRSVRR8D5RY943QM7D4","permalink":"https:\/\/randomly.cluxnei.dev\/r\/YFSX4MXTRSVRR8D5RY943QM7D4?g=equations.sequence&v=1&p=eyJjb3VudCI6NSwia2luZCI6Im1peGVkIiwidGVybXMiOjV9&s=random-org"},"uses_entropy":true,"reproducible":true}