MathsCBSE Class 10 · Standard · Board exam 2026, set 30/3/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 22(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/3/1, section B, question 22(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 2 marks · Very short answerArithmetic Progressions

In an A.P., the first term is 32 and the last term is -10. If the common difference is -2, then find the number of terms and their sum.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/3/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The last term is $a_{n}$ . Use $a_{n} = a + (n - 1) d$ to find n.

Hint 2

Once you know n, use $S_{n} = \frac{n}{2} (a + l)$ .

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Here $a = 32$ , $l = a_{n} = - 10$ , $d = - 2$ . Using $a_{n} = a + (n - 1) d$ : $32 + (n - 1) (- 2) = - 10$ .
½ mark
$(n - 1) (- 2) = - 42 \Rightarrow n - 1 = 21 \Rightarrow n = 22$ .
½ mark
$S_{n} = \frac{n}{2} (a + l)$ , so $S_{22} = \frac{22}{2} [32 + (- 10)]$ .
½ mark
$S_{22} = 11 \times 22 = 242$ . There are 22 terms and their sum is 242.
½ mark

Answer: n = 22, sum = 242

Where the marks are

Writes $32 + (n - 1) (- 2) = - 10$ (½ mark)
Gets n = 22 (½ mark)
Uses $S_{22} = \frac{22}{2} (32 - 10)$ (½ mark)
Gets sum = 242 (½ mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/3/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 22(a)

Hints

Step-by-step solution

Revise the chapter

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