| { |
| "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" |
| } |
| ] |
| } |
|
|
