Arithmetic Progressions
Karnataka Board · Class 10 · Mathematics
Flashcards for Arithmetic Progressions — Karnataka Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
Find the 15th term of the AP: 3, 7, 11, 15, ...
Answer
Step 1: Identify a = 3, d = 7-3 = 4, n = 15 Step 2: Use formula aₙ = a + (n-1)d Step 3: a₁₅ = 3 + (15-1)×4 = 3 + 14×4 = 3 + 56 = 59 Answer: 59
Which term of the AP 5, 9, 13, 17, ... is 81?
Answer
Step 1: Given a = 5, d = 9-5 = 4, aₙ = 81 Step 2: Use aₙ = a + (n-1)d Step 3: 81 = 5 + (n-1)×4 Step 4: 76 = (n-1)×4 Step 5: n-1 = 19, so n = 20 Answer: 20th term
Find the sum of first 20 terms of AP: 2, 5, 8, 11, ...
Answer
Step 1: Identify a = 2, d = 5-2 = 3, n = 20 Step 2: Use Sₙ = n/2[2a + (n-1)d] Step 3: S₂₀ = 20/2[2×2 + (20-1)×3] Step 4: S₂₀ = 10[4 + 19×3] = 10[4 + 57] = 10×61 = 610 Answer: 610
Check if -150 is a term of AP: 11, 8, 5, 2, ...
Answer
Step 1: Find a = 11, d = 8-11 = -3 Step 2: Assume aₙ = -150 Step 3: -150 = 11 + (n-1)(-3) Step 4: -161 = (n-1)(-3) Step 5: n-1 = 161/3 = 53.67... Step 6: Since n must be a whole number, -150 is NOT a
Find three numbers in AP whose sum is 27 and product is 504.
Answer
Step 1: Let numbers be (a-d), a, (a+d) Step 2: Sum: (a-d) + a + (a+d) = 27, so 3a = 27, a = 9 Step 3: Numbers are (9-d), 9, (9+d) Step 4: Product: (9-d)×9×(9+d) = 504 Step 5: 9(81-d²) = 504, so 81-d²
How many terms of AP 24, 21, 18, ... give sum 78?
Answer
Step 1: a = 24, d = 21-24 = -3, Sₙ = 78 Step 2: Use Sₙ = n/2[2a + (n-1)d] Step 3: 78 = n/2[48 + (n-1)(-3)] Step 4: 156 = n[48 - 3n + 3] = n[51 - 3n] Step 5: 3n² - 51n + 156 = 0, or n² - 17n + 52 = 0 S
When do you use the formula aₙ = a + (n-1)d?
Answer
Use when finding the nth term of an AP. Given: First term (a), common difference (d), position (n) Example: For AP 7, 10, 13, 16, ... find 8th term a = 7, d = 3, n = 8 a₈ = 7 + (8-1)×3 = 7 + 21 = 28
A salary starts at ₹8000 with ₹500 annual increment. Find salary in 10th year.
Answer
Step 1: This forms AP with a = 8000, d = 500 Step 2: Need 10th term, so n = 10 Step 3: a₁₀ = a + (n-1)d Step 4: a₁₀ = 8000 + (10-1)×500 Step 5: a₁₀ = 8000 + 9×500 = 8000 + 4500 = 12500 Answer: ₹12,500
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Arithmetic Progressions covers several key topics that are frequently asked in Karnataka Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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