Arithmetic Progressions
NIOS · Class 10 · Maths
Flashcards for Arithmetic Progressions — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
Interactive on Super Tutor
Studying Arithmetic Progressions? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.
1,000+ Class 10 students started this chapter today
Super Tutor has 7+ illustrations like this for Arithmetic Progressions alone — flashcards, concept maps, and step-by-step visuals.
See them allCheck if the sequence 3, 7, 11, 15, 19, ... is an AP. If yes, find the first term and common difference.
Answer
Step 1: Calculate differences between consecutive terms: 7 - 3 = 4 11 - 7 = 4 15 - 11 = 4 19 - 15 = 4 Step 2: Since all differences are equal (= 4), it is an AP. Step 3: First term (a) = 3, Common dif…
Find the 12th term of the AP: 5, 8, 11, 14, ...
Answer
Step 1: Identify given values a = 5, d = 8 - 5 = 3, n = 12 Step 2: Use formula tn = a + (n-1)d t₁₂ = 5 + (12-1) × 3 Step 3: Calculate t₁₂ = 5 + 11 × 3 = 5 + 33 = 38 Answer: 12th term = 38…
The 5th term of an AP is 23 and the 8th term is 32. Find the first term and common difference.
Answer
Step 1: Write given information t₅ = 23, t₈ = 32 Step 2: Use formula tn = a + (n-1)d t₅ = a + 4d = 23 ... (1) t₈ = a + 7d = 32 ... (2) Step 3: Subtract equation (1) from (2) 3d = 9, so d = 3 Step 4: S…
Which term of the AP 7, 10, 13, 16, ... is 40?
Answer
Step 1: Identify values a = 7, d = 10 - 7 = 3, tn = 40 Step 2: Use formula tn = a + (n-1)d 40 = 7 + (n-1) × 3 Step 3: Solve for n 40 = 7 + 3n - 3 40 = 4 + 3n 36 = 3n n = 12 Step 4: Verify: t₁₂ = 7 + 1…
Find the sum of first 15 terms of the AP: 4, 7, 10, 13, ...
Answer
Step 1: Identify values a = 4, d = 7 - 4 = 3, n = 15 Step 2: Use formula Sn = n/2[2a + (n-1)d] S₁₅ = 15/2[2(4) + (15-1) × 3] Step 3: Calculate inside brackets S₁₅ = 15/2[8 + 14 × 3] S₁₅ = 15/2[8 + 42]…
How many terms of the AP 6, 10, 14, 18, ... are needed to get a sum of 252?
Answer
Step 1: Identify values a = 6, d = 10 - 6 = 4, Sn = 252 Step 2: Use formula Sn = n/2[2a + (n-1)d] 252 = n/2[2(6) + (n-1) × 4] 252 = n/2[12 + 4n - 4] 252 = n/2[8 + 4n] Step 3: Simplify 504 = n(8 + 4n) …
Find the sum: 5 + 11 + 17 + 23 + ... + 95
Answer
Step 1: Identify the AP a = 5, d = 11 - 5 = 6, last term l = 95 Step 2: Find number of terms using tn = a + (n-1)d 95 = 5 + (n-1) × 6 90 = 6(n-1) n - 1 = 15 n = 16 Step 3: Use sum formula Sn = n/2(a +…
The first three terms of an AP are (x+1), (2x-1), and (3x+1). Find x and the three terms.
Answer
Step 1: For AP, common difference must be same d₁ = (2x-1) - (x+1) = x - 2 d₂ = (3x+1) - (2x-1) = x + 2 Step 2: Set d₁ = d₂ x - 2 = x + 2 This gives -2 = 2, which is impossible. Step 3: Check if middl…
+12 more flashcards available
Practice AllFrequently Asked Questions
What are the important topics in Arithmetic Progressions for NIOS Class 10 Maths?
How to score full marks in Arithmetic Progressions — NIOS Class 10 Maths?
How many flashcards are available for Arithmetic Progressions?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Arithmetic Progressions
Important Questions
Practice with board exam-style questions
Syllabus
What topics to cover
Revision Notes
Key points for last-minute revision
Study Plan
Step-by-step plan to ace this chapter
Formula Sheet
All formulas in one place
Chapter Summary
Understand the chapter at a glance
Practice Quiz
Test yourself with a quick quiz
Concept Maps
See how topics connect visually
For serious students
Get the full Arithmetic Progressions chapter — for free.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for NIOS Class 10 Maths.