| { |
| "schemaVersion": 1, |
| "chapterId": "math-p1-c3", |
| "slug": "arithmetic-sequences-algebra", |
| "subject": "maths", |
| "title": "Arithmetic Sequences and Algebra", |
| "practiceLabel": "sample", |
| "source": "SCERT Kerala SSLC Mathematics 2025 raw extract (math-ch3-seqalg-raw.txt). Practice is labelled sample — not board-certified.", |
| "shortNotes": [ |
| "The term at every position is twice the number giving the position:", |
| "Position 1 2 3 ...", |
| "Term 2 × 1 = 2 2 × 2 = 4 2 × 3 = 6 ...", |
| "The term at every position is one less than twice the number giving the position:", |
| "Term (2 × 1) − 1 = 1 (2 × 2) − 1 = 3 (2 × 3) − 1 = 5 ...", |
| "We can use algebra to concisely state these.", |
| "Thus we can describe the first sequence like this:", |
| "The number in the nth position is 2n", |
| "The number in the nth position is 2n − 1" |
| ], |
| "definitions": [], |
| "formulas": [ |
| "Term 2 × 1 = 2 2 × 2 = 4 2 × 3 = 6 ...", |
| "Term (2 × 1) − 1 = 1 (2 × 2) − 1 = 3 (2 × 3) − 1 = 5 ...", |
| "The sequence 2, 4, 6, ... of even numbers: xn = 2n", |
| "The sequence 1, 3, 5, ... of odd numbers: yn = 2n – 1", |
| "the 10th term is 10 − 1 = 9", |
| "(iv) The 10th term is 12 + (9 × 11) = 111", |
| "(ii) The nth term is 12 + ((n − 1) × 11) = 12 + 11(n − 1)", |
| "11(n − 1) = 11n − 11", |
| "12 + 11(n − 1) = 12 + (11n − 11) = 11n + 1", |
| "xn = 11n + 1" |
| ], |
| "commonMistakes": [ |
| "Using the nth-term formula when the question asks for a sum, or the reverse.", |
| "Skipping the diagram or given data before substituting.", |
| "Arithmetic slips in substitution after writing the correct formula." |
| ], |
| "sampleQuestions": [ |
| { |
| "id": "arithmetic-sequences-algebra-q1", |
| "marks": 2, |
| "question": "definite rule. How do we state this rule?", |
| "answer": "Sample practice — write the definition or working from the textbook method.", |
| "label": "sample" |
| }, |
| { |
| "id": "arithmetic-sequences-algebra-q2", |
| "marks": 2, |
| "question": "For example, how do we describe the sequence 2, 4, 6, ... of even numbers?", |
| "answer": "Sample practice — write the definition or working from the textbook method.", |
| "label": "sample" |
| }, |
| { |
| "id": "arithmetic-sequences-algebra-q3", |
| "marks": 2, |
| "question": "What about the sequence 1, 3, 5, ... of odd numbers?", |
| "answer": "Sample practice — write the definition or working from the textbook method.", |
| "label": "sample" |
| }, |
| { |
| "id": "arithmetic-sequences-algebra-q4", |
| "marks": 2, |
| "question": "compute the 10th term of this sequence?", |
| "answer": "Sample practice — write the definition or working from the textbook method.", |
| "label": "sample" |
| }, |
| { |
| "id": "arithmetic-sequences-algebra-q5", |
| "marks": 2, |
| "question": "In general how do we write the nth term?", |
| "answer": "Sample practice — write the definition or working from the textbook method.", |
| "label": "sample" |
| }, |
| { |
| "id": "arithmetic-sequences-algebra-q6", |
| "marks": 2, |
| "question": "How do we compute its nth term?", |
| "answer": "Sample practice — write the definition or working from the textbook method.", |
| "label": "sample" |
| }, |
| { |
| "id": "arithmetic-sequences-algebra-q7", |
| "marks": 2, |
| "question": "adding a fixed number ?", |
| "answer": "Sample practice — write the definition or working from the textbook method.", |
| "label": "sample" |
| }, |
| { |
| "id": "arithmetic-sequences-algebra-q8", |
| "marks": 2, |
| "question": "So, what can we say in general?", |
| "answer": "Sample practice — write the definition or working from the textbook method.", |
| "label": "sample" |
| } |
| ] |
| } |
|
|
