Arithmetic Progressions
Punjab Board · Class 10 · Mathematics
Flashcards for Arithmetic Progressions — Punjab Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allIdentify whether 5, 10, 15, 20, 25, ... forms an AP. If yes, find the common difference.
Answer
Step 1: Check if consecutive terms have a constant difference. Step 2: Calculate a₂ - a₁ = 10 - 5 = 5 Step 3: Calculate a₃ - a₂ = 15 - 10 = 5 Step 4: Calculate a₄ - a₃ = 20 - 15 = 5 Step 5: Since all …
Is -2, 2, -2, 2, -2, ... an arithmetic progression? Justify your answer.
Answer
Step 1: Check the difference between consecutive terms. Step 2: a₂ - a₁ = 2 - (-2) = 4 Step 3: a₃ - a₂ = -2 - 2 = -4 Step 4: Since a₂ - a₁ ≠ a₃ - a₂ (4 ≠ -4), the difference is NOT constant. Step 5: W…
Write the first four terms of an AP where a = 3 and d = 2.
Answer
Step 1: First term a₁ = a = 3 Step 2: Second term a₂ = a + d = 3 + 2 = 5 Step 3: Third term a₃ = a + 2d = 3 + 2(2) = 3 + 4 = 7 Step 4: Fourth term a₄ = a + 3d = 3 + 3(2) = 3 + 6 = 9 Answer: The first …
For the AP: 2, 7, 12, 17, ... identify a and d, then find the 8th term.
Answer
Step 1: Identify first term a = 2 Step 2: Find common difference d = 7 - 2 = 5 Step 3: Use formula aₙ = a + (n - 1)d Step 4: For 8th term, n = 8, so a₈ = 2 + (8 - 1)(5) Step 5: a₈ = 2 + 7(5) = 2 + 35 …
Find the 15th term of the AP: -3, -2, -1, 0, ...
Answer
Step 1: Identify a = -3 Step 2: Find d = -2 - (-3) = -2 + 3 = 1 Step 3: Use aₙ = a + (n - 1)d Step 4: For n = 15: a₁₅ = -3 + (15 - 1)(1) Step 5: a₁₅ = -3 + 14(1) = -3 + 14 = 11 Answer: The 15th term i…
Which term of the AP: 5, 8, 11, 14, ... equals 32?
Answer
Step 1: Identify a = 5, d = 8 - 5 = 3 Step 2: We need to find n such that aₙ = 32 Step 3: Use aₙ = a + (n - 1)d Step 4: 32 = 5 + (n - 1)(3) Step 5: 32 - 5 = (n - 1)(3) Step 6: 27 = (n - 1)(3) Step 7: …
Is 101 a term of the AP: 3, 7, 11, 15, ...? Show your working.
Answer
Step 1: Identify a = 3, d = 7 - 3 = 4 Step 2: Assume 101 is the nth term, so aₙ = 101 Step 3: Use aₙ = a + (n - 1)d Step 4: 101 = 3 + (n - 1)(4) Step 5: 101 - 3 = (n - 1)(4) Step 6: 98 = (n - 1)(4) St…
A person saves ₹100 in the first month, ₹150 in the second month, ₹200 in the third month, and so on. Is this an AP? If yes, find the savings in the 12th month.
Answer
Step 1: List the savings sequence: 100, 150, 200, ... Step 2: Check differences: 150 - 100 = 50, 200 - 150 = 50 Step 3: Since d = 50 is constant, this IS an AP with a = 100, d = 50 Step 4: For 12th mo…
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