Arithmetic Progressions — Flashcards
Karnataka Board · Class 10 · Mathematics
20 flashcards for Arithmetic Progressions (Karnataka Board Class 10 Mathematics) to test yourself on key terms and facts.
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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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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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