5-44f8-b1f3-cfe46837efd3","questionNumber":"1","questionType":"LA","specification":"","difficulty":1,"totalMarks":5,"sourceTitle":"Sequences (Higher)","parts":[{"id":"af545ff9-6ca9-4104-9eea-39b758dc3660","label":"","content":"The 4th term of an arithmetic series is 17 \nThe 10th term of the same arithmetic series is 35 \nFind the sum of the first 50 terms of this arithmetic series.","markscheme":"- Formulates two equations for the terms: $a + 3d = 17$ and $a + 9d = 35$ M1\n- Solves for common difference $d = 3$ M1\n- Solves for first term $a = 8$ M1\n- Substitutes $a$, $d$, and $n=50$ into the sum formula $S_n = \\frac{n}{2}(2a + (n-1)d)$ M1\n- Final answer 4075 A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Sets up simultaneous equations for the 4th and 10th terms using $a + (n-1)d$.","code":"M"},{"id":"p2","marks":1,"description":"Correctly calculates the common difference $d = 3$.","code":"M"},{"id":"p3","marks":1,"description":"Correctly calculates the first term $a = 8$.","code":"M"},{"id":"p4","marks":1,"description":"Correctly substitutes values into the arithmetic series sum formula.","code":"M"},{"id":"p5","marks":1,"description":"Final answer of 4075.","code":"A"}],"finalAnswers":["4075"],"generatedAt":"2026-05-07T02:11:27.220Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"fb470127-3e1e-4d6f-b8e1-aab9975c7b41","revisionId":"c9b000e9-ffd3-4206-9fed-e636780f7d91","questionNumber":"2","questionType":"LA","specification":"","difficulty":1,"totalMarks":5,"sourceTitle":"Sequences (Higher)","parts":[{"id":"0e580a94-f666-4f1b-99c5-0c96ae32768a","label":"","content":"The sum of the first 48 terms of an arithmetic series is 4 times the sum of the first 36 terms of the same series. \nFind the sum of the first 30 terms of this series.","markscheme":"- Sets up the equation $S_{48} = 4(S_{36})$ using the sum formula M1\n- Expands and simplifies: $24(2a + 47d) = 72(2a + 35d)$ M1\n- Simplifies to find a relationship between $a$ and $d$, e.g., $2a + 29d = 0$ M1\n- Recognises that $S_{30} = 15(2a + 29d)$ M1\n- Final answer 0 A1","marks":5,"order":0,"markingRubric":{"totalMarks":5,"points":[{"id":"p1","marks":1,"description":"Correctly applies the sum formula to both $S_{48}$ and $S_{36}$.","code":"M"},{"id":"p2","marks":1,"description":"Equates $S_{48}$ to $4 \\times S_{36}$ and begins simplification.","code":"M"},{"id":"p3","marks":1,"description":"Simplifies the equation to reach $2a + 29d = 0$ or equivalent.","code":"M"},{"id":"p4","marks":1,"description":"Identifies that the expression for $S_{30}$ contains the factor $(2a + 29d)$.","code":"M"},{"id":"p5","marks":1,"description":"Final answer of 0.","code":"A"}],"finalAnswers":["0"],"generatedAt":"2026-05-07T02:11:27.220Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"0900cc55-1d40-42fe-bb15-472d8077ab99","revisionId":"f86fbab5-b8e6-40da-a209-46cd78d23b2e","questionNumber":"3","questionType":"LA","specification":"","difficulty":1,"totalMarks":2,"sourceTitle":"Sequences (Higher)","parts":[{"id":"7f6007e8-21fe-470c-8ac9-bc77a9ef3844","label":"","content":"Here are the first five terms of an arithmetic sequence.\n\n7 10 13 16 19\n\nFind the sum of the first 100 terms of this sequence.","markscheme":"- Identifies $a = 7$ and $d = 3$ and substitutes into $S_n = \\frac{n}{2}(2a + (n-1)d)$ M1\n- Final answer 15550 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Identifies $a=7, d=3$ and substitutes into the sum formula for $n=100$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 15550.","code":"A"}],"finalAnswers":["15550"],"generatedAt":"2026-05-07T02:11:27.220Z","modelVersion":"gemini-3-flash-preview"}}],"options":[]},{"id":"48a4915b-ca6c-4d82-aaa9-1da6afab8afc","revisionId":"3eef9e9d-ed46-4025-85fe-2740a8fbdbc8","questionNumber":"4","ques