{"generator":"equations.sequence","version":1,"value":{"problems":[{"prompt":"1, -2, 4, -8, 16, \u2026","prompt_latex":"1,\\; -2,\\; 4,\\; -8,\\; 16,\\; \\ldots","answer":"-32   (geometric, ratio -2)","answer_latex":"-32","kind":"geometric","rule":"geometric, ratio -2","terms":[1,-2,4,-8,16],"next":-32},{"prompt":"-7, -13, -21, -31, -43, \u2026","prompt_latex":"-7,\\; -13,\\; -21,\\; -31,\\; -43,\\; \\ldots","answer":"-57   (quadratic, second difference -2)","answer_latex":"-57","kind":"quadratic","rule":"quadratic, second difference -2","terms":[-7,-13,-21,-31,-43],"next":-57},{"prompt":"-9, -18, -33, -54, -81, \u2026","prompt_latex":"-9,\\; -18,\\; -33,\\; -54,\\; -81,\\; \\ldots","answer":"-114   (quadratic, second difference -6)","answer_latex":"-114","kind":"quadratic","rule":"quadratic, second difference -6","terms":[-9,-18,-33,-54,-81],"next":-114},{"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":"6, 1, 7, 8, 15, \u2026","prompt_latex":"6,\\; 1,\\; 7,\\; 8,\\; 15,\\; \\ldots","answer":"23   (each term is the sum of the two before it)","answer_latex":"23","kind":"fibonacci","rule":"each term is the sum of the two before it","terms":[6,1,7,8,15],"next":23}],"count":5},"display":"1. 1, -2, 4, -8, 16, \u2026   \u2192   -32   (geometric, ratio -2)\n2. -7, -13, -21, -31, -43, \u2026   \u2192   -57   (quadratic, second difference -2)\n3. -9, -18, -33, -54, -81, \u2026   \u2192   -114   (quadratic, second difference -6)\n4. 4, 8, 16, 32, 64, \u2026   \u2192   128   (geometric, ratio 2)\n5. 6, 1, 7, 8, 15, \u2026   \u2192   23   (each term is the sum of the two before it)","meta":{"latex":[["1,\\; -2,\\; 4,\\; -8,\\; 16,\\; \\ldots","-32"],["-7,\\; -13,\\; -21,\\; -31,\\; -43,\\; \\ldots","-57"],["-9,\\; -18,\\; -33,\\; -54,\\; -81,\\; \\ldots","-114"],["4,\\; 8,\\; 16,\\; 32,\\; 64,\\; \\ldots","128"],["6,\\; 1,\\; 7,\\; 8,\\; 15,\\; \\ldots","23"]],"problems":5,"stream_bytes_used":20,"rejections":3,"entropy_in_bytes":16,"duration_us":216},"receipt":{"source":"csprng","source_label":"Operating System CSPRNG","class":"A","class_label":"Cryptographic","caveat":null,"narrative":"Drawn from the kernel entropy pool on the server that rendered this page. (The source you picked was unreachable, so we fell back to the kernel.)","proof_url":null,"reference":null,"observed_at":"2026-09-13T19:20:17+00:00","degraded":true,"mixed_with_csprng":false,"latency_ms":1507,"cached":false},"seed":{"token":"C0R7ZQB5DDXTQW2ZNRGC5C0GZ4","permalink":"https:\/\/randomly.cluxnei.dev\/r\/C0R7ZQB5DDXTQW2ZNRGC5C0GZ4?g=equations.sequence&v=1&p=eyJjb3VudCI6NSwia2luZCI6Im1peGVkIiwidGVybXMiOjV9&s=csprng"},"uses_entropy":true,"reproducible":true}