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Important Questions

Arithmetic Progressions

Gujarat Board · Class 10 · Mathematics

Most important questions from Arithmetic Progressions for Gujarat Board Class 10 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

45 questions22 flashcards5 concepts

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Illustrates the structure of an Arithmetic Progression (A.P.), showing the first term 'a' and common difference 'd', along with the general term formula.
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45 Questions·
multiple choicemultiple correct

Sample Questions

1multiple correct

Which of the following sequences are arithmetic progressions? (Select all correct answers)

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2, 5, 8, 11, 14, ..., 10, 7, 4, 1, -2, ..., 5, 5, 5, 5, 5, ...

For a sequence to be an AP, the difference between consecutive terms must be constant. Option 1: d = 3 (AP), Option 2: differences are 3,5,7,9 (not AP), Option 3: d = -3 (AP), Option 4: d = 0 (AP), Option 5: differences are 2,4,8,16 (not AP).

2multiple choice

Find the number of terms in the AP: 7, 10, 13, ..., 43

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13

Given: a = 7, d = 3, last term = 43. Using an = a + (n-1)d: 43 = 7 + (n-1)×3. Solving: 43 - 7 = (n-1)×3, so 36 = (n-1)×3, thus n-1 = 12, therefore n = 13.

3multiple choice

The sum of first n natural numbers 1 + 2 + 3 + ... + n is:

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n(n+1)/2

Natural numbers 1, 2, 3, ..., n form an AP with a = 1, d = 1. Using S = n/2[2a + (n-1)d]: S = n/2[2×1 + (n-1)×1] = n/2[2 + n - 1] = n/2[n + 1] = n(n+1)/2.

4multiple correct

Which of the following are correct statements about arithmetic progressions? (Select all correct answers)

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The common difference can be negative, The common difference can be zero, The nth term formula is an = a + (n-1)d

The common difference d can be positive, negative, or zero. An AP can have any number of terms (finite or infinite). The nth term formula an = a + (n-1)d is correct. Terms in an AP can be positive, negative, or zero.

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Frequently Asked Questions

What are the important topics in Arithmetic Progressions for Gujarat Board Class 10 Mathematics?
Key topics in Arithmetic Progressions include Arithmetic Progressions Problem-Solving Decision Tree, Arithmetic Progressions — Complete Concept Map, Mind map showing different categories of real-life arithmetic progressions with their characteristics. These are the concepts Gujarat Board Class 10 examiners draw on most — study them first, then practise related questions.
How to score full marks in Arithmetic Progressions — Gujarat Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Arithmetic Progressions?
There are 45 practice questions available for Arithmetic Progressions. These cover multiple question types including MCQs, short answer, and long answer questions.

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