{
  "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"
    }
  ]
}