Arithmetic Progressions
Gujarat Board · Class 10 · Mathematics
Flashcards for Arithmetic Progressions — Gujarat Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allCheck if the following list forms an AP: 5, 10, 15, 20, 25, ... If yes, find the first term and common difference.
Answer
Step 1: Check differences between consecutive terms. - a₂ - a₁ = 10 - 5 = 5 - a₃ - a₂ = 15 - 10 = 5 - a₄ - a₃ = 20 - 15 = 5 - a₅ - a₄ = 25 - 20 = 5 Step 2: Since all differences equal 5, this IS an A…
Check if 2, 4, 8, 16, 32, ... forms an AP. Explain why or why not.
Answer
Step 1: Calculate differences between consecutive terms. - a₂ - a₁ = 4 - 2 = 2 - a₃ - a₂ = 8 - 4 = 4 - a₄ - a₃ = 16 - 8 = 8 - a₅ - a₄ = 32 - 16 = 16 Step 2: The differences are 2, 4, 8, 16, ... (not …
Reena gets a starting salary of ₹8000 with an annual increment of ₹500. Write the AP for her salary for the first 5 years and find the common difference.
Answer
Step 1: First year salary = ₹8000 Second year salary = ₹8000 + ₹500 = ₹8500 Third year salary = ₹8500 + ₹500 = ₹9000 Fourth year salary = ₹9000 + ₹500 = ₹9500 Fifth year salary = ₹9500 + ₹500 = ₹10000…
Formula for nth term of an AP: Write the formula and explain what each symbol means.
Answer
Formula: aₙ = a + (n - 1)d Where: - aₙ = the nth term (general term) - a = first term of the AP - d = common difference - n = position of the term in the sequence Example: In AP 3, 7, 11, 15, ... a …
Find the 10th term of the AP: 2, 5, 8, 11, ...
Answer
Step 1: Identify the values. a (first term) = 2 d (common difference) = 5 - 2 = 3 n = 10 Step 2: Apply formula aₙ = a + (n - 1)d a₁₀ = 2 + (10 - 1)×3 a₁₀ = 2 + 9×3 a₁₀ = 2 + 27 a₁₀ = 29 Answer: The …
Find the 15th term of the AP: 100, 70, 40, 10, ...
Answer
Step 1: Identify the values. a (first term) = 100 d (common difference) = 70 - 100 = -30 n = 15 Step 2: Apply formula aₙ = a + (n - 1)d a₁₅ = 100 + (15 - 1)×(-30) a₁₅ = 100 + 14×(-30) a₁₅ = 100 - 420…
In an AP, if a = 3, d = 2, and aₙ = 23, find n (which term is 23?).
Answer
Step 1: Use formula aₙ = a + (n - 1)d 23 = 3 + (n - 1)×2 Step 2: Solve for n. 23 = 3 + 2n - 2 23 = 1 + 2n 22 = 2n n = 11 Step 3: Verify. a₁₁ = 3 + (11 - 1)×2 = 3 + 20 = 23 ✓ Answer: n = 11 (23 is t…
Formula for sum of first n terms of an AP: Write both forms and explain when to use each.
Answer
Formula 1: S = n/2 [2a + (n - 1)d] Where: - S = sum of first n terms - a = first term - d = common difference - n = number of terms Use when: You know a, d, and n Formula 2: S = n/2 (a + l) Where:…
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