{
  "schemaVersion": 1,
  "chapterId": "math-p1-c1",
  "slug": "arithmetic-sequences",
  "subject": "maths",
  "title": "Arithmetic Sequences",
  "practiceLabel": "sample",
  "source": "SCERT Kerala SSLC Mathematics 2025 raw extract (math-ch1-raw.txt). Practice is labelled sample — not board-certified.",
  "shortNotes": [
    "according to some rule, is called a number sequence.",
    "and again, is called an arithmetic sequence",
    "This number, got by subtracting the previous term from any term, is called the common",
    "Halves of natural numbers 2",
    "Squares of natural numbers 1, 4, 9, ...",
    "A collection of numbers, which are ordered as the first, second, third and so on like this,",
    "Such sequences often arise in computing various measurements. For example, if we",
    "As another example, look at these pictures:",
    "Mathematics Part - I",
    "If we write down the length of the hypotenuse of"
  ],
  "definitions": [
    {
      "term": "according to some rule,",
      "definition": "according to some rule, is called a number sequence."
    },
    {
      "term": "and again,",
      "definition": "and again, is called an arithmetic sequence"
    },
    {
      "term": "number, got by subtracting the previous term from any term,",
      "definition": "This number, got by subtracting the previous term from any term, is called the common"
    }
  ],
  "formulas": [
    "n = 2, 3, 4, 5 we get the same numbers",
    "2, 4, 8, 16. From n = 6 onwards, the",
    "7 – 3 = 4 times",
    "(ii) The number added is 73 – 37 = 36",
    "(iv) Common difference is 36 ÷ 4 = 9",
    "3 − 1 = 2 times",
    "(ii) The 1st term is 37 − (2 × 9) = 19",
    "(i) From the 3rd to the 10th, position increases by 10 − 3 = 7",
    "(iii) The 10th term is 37 + (7 × 9) = 100",
    "(i) From the 1st to the 10th, position increases by 10 − 1 = 9"
  ],
  "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-q1",
      "marks": 2,
      "question": "get? What if we change it to 2n + 1?",
      "answer": "Sample practice — write the definition or working from the textbook method.",
      "label": "sample"
    },
    {
      "id": "arithmetic-sequences-q2",
      "marks": 2,
      "question": "triangles in each picture?",
      "answer": "Sample practice — write the definition or working from the textbook method.",
      "label": "sample"
    },
    {
      "id": "arithmetic-sequences-q3",
      "marks": 2,
      "question": "How about five points?",
      "answer": "Sample practice — write the definition or working from the textbook method.",
      "label": "sample"
    },
    {
      "id": "arithmetic-sequences-q4",
      "marks": 2,
      "question": "What is the next number in this?",
      "answer": "Sample practice — write the definition or working from the textbook method.",
      "label": "sample"
    },
    {
      "id": "arithmetic-sequences-q5",
      "marks": 2,
      "question": "Now what if we take halves of natural numbers?",
      "answer": "Sample practice — write the definition or working from the textbook method.",
      "label": "sample"
    },
    {
      "id": "arithmetic-sequences-q6",
      "marks": 2,
      "question": "What if we start with 10 and subtract 3 at every step?",
      "answer": "Sample practice — write the definition or working from the textbook method.",
      "label": "sample"
    },
    {
      "id": "arithmetic-sequences-q7",
      "marks": 2,
      "question": "What's the moral of this?",
      "answer": "Sample practice — write the definition or working from the textbook method.",
      "label": "sample"
    },
    {
      "id": "arithmetic-sequences-q8",
      "marks": 2,
      "question": "(i) How many small squares are there in each picture?",
      "answer": "Sample practice — write the definition or working from the textbook method.",
      "label": "sample"
    }
  ]
}