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Arithmetic Progressions — Flashcards

NIOS · Class 10 · Maths

25 flashcards for Arithmetic Progressions (NIOS Class 10 Maths) to test yourself on key terms and facts. Part of the NIOS Class 10 Maths syllabus.

29 questions25 flashcards6 formulas & key relations5 concepts

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An illustration showing various real-world examples of number patterns, such as petals of a flower, holes in a honeycomb, spirals on a pineapple, and a simple bar chart showing increasing bank deposit
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One of 7 illustrations for Arithmetic Progressions in Super Tutor — alongside flashcards, concept maps and practice questions.

25 Flashcards·
Identifying an APnth term of APFinding common differenceFinding first termUnderstanding formula
Card 1Identifying an AP

Find whether the sequence 2, 7, 12, 17, 22, ... is an AP. If yes, find a and d.

Answer

Step 1: Find consecutive differences. 7 - 2 = 5 12 - 7 = 5 17 - 12 = 5 22 - 17 = 5 Step 2: The difference is constant, so it is an AP. Step 3: First term a = 2 and common difference d = 5. Answer: It …

Card 2Identifying an AP

Find whether the sequence 3, 7, 12, 18, 25, ... is an AP.

Answer

Step 1: Find consecutive differences. 7 - 3 = 4 12 - 7 = 5 18 - 12 = 6 25 - 18 = 7 Step 2: The differences are not the same. Answer: It is not an AP.

Card 3nth term of AP

Find the nth term of the AP 5, 9, 13, 17, ...

Answer

Step 1: Identify a and d. a = 5, d = 4 Step 2: Use the nth term formula. tn = a + (n - 1)d Step 3: Substitute values. tn = 5 + (n - 1)4 Step 4: Simplify. tn = 5 + 4n - 4 = 4n + 1 Answer: tn = 4n + 1.

Card 4nth term of AP

Find the 15th term of the AP 16, 11, 6, 1, -4, ...

Answer

Step 1: Identify a and d. a = 16, d = 11 - 16 = -5 Step 2: Use tn = a + (n - 1)d. Step 3: Substitute n = 15. t15 = 16 + (15 - 1)(-5) Step 4: Simplify. t15 = 16 + 14(-5) = 16 - 70 = -54 Answer: The 15t…

Card 5Finding common difference

The first term of an AP is -3 and the 12th term is 41. Find the common difference.

Answer

Step 1: Use tn = a + (n - 1)d. Step 2: Substitute a = -3, n = 12, t12 = 41. 41 = -3 + (12 - 1)d 41 = -3 + 11d Step 3: Solve. 44 = 11d d = 4 Answer: The common difference is 4.

Card 6Finding first term

The common difference of an AP is 5 and the 10th term is 43. Find the first term.

Answer

Step 1: Use tn = a + (n - 1)d. Step 2: Substitute t10 = 43, d = 5. 43 = a + (10 - 1)5 43 = a + 45 Step 3: Solve. a = 43 - 45 = -2 Answer: The first term is -2.

Card 7nth term of AP

The first term of an AP is -2 and the 11th term is 18. Find the 15th term.

Answer

Step 1: Find d first. t11 = a + (11 - 1)d 18 = -2 + 10d 20 = 10d d = 2 Step 2: Find t15. t15 = a + (15 - 1)d t15 = -2 + 14(2) t15 = -2 + 28 = 26 Answer: The 15th term is 26.

Card 8Understanding formula

Why is the nth term formula tn = a + (n - 1)d true?

Answer

An AP starts with a. Each next term adds the same difference d. 1st term: a 2nd term: a + d 3rd term: a + 2d 4th term: a + 3d So the nth term has added d exactly (n - 1) times. That gives tn = a + (n …

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Frequently Asked Questions

What are the important topics in Arithmetic Progressions for NIOS Class 10 Maths?
Key topics in Arithmetic Progressions include Identifying an Arithmetic Progression, General Term of an AP, Finding Unknown Terms, a, or d, Sum of First n Terms. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How many flashcards are available for Arithmetic Progressions?
There are 25 flashcards for Arithmetic Progressions covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Arithmetic Progressions for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 29 practice questions on Arithmetic Progressions. Revise definitions regularly and use flashcards for quick recall before the exam.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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