MathsCBSE Class 10 · Basic · Board exam 2026, set 430/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2026: question 28(a)

Set in the CBSE Class 10 board exam of 2026, paper 430/5/1, section C, question 28(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(a) · 3 marks · Short answerArithmetic Progressions

In an A.P., it is given that $a = 2$ , $d = 8$ and $S_{n} = 90$ . Find the value of $n$ .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/5/1.

Hints

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

Hint 1

Use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ and set it equal to 90.

Hint 2

You will get a quadratic in n; remember n must be a positive integer.

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.

$S_{n} = \frac{n}{2} [2 a + (n - 1) d] \Rightarrow \frac{n}{2} [4 + (n - 1) 8] = 90$
1 mark
$n (4 n - 2) = 90 \Rightarrow 4 n^{2} - 2 n - 90 = 0 \Rightarrow 2 n^{2} - n - 45 = 0$
1 mark
$(n - 5) (2 n + 9) = 0 \Rightarrow n = 5$ or $n = - \frac{9}{2}$ (rejected, as $n$ is a natural number). So $n = 5$ .
1 mark

Answer: $n = 5$

Where the marks are

Correct substitution in $S_{n}$ formula (1 mark)
Forms $2 n^{2} - n - 45 = 0$ (1 mark)
Solves, rejects $- \frac{9}{2}$ , gets $n = 5$ (1 mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)
Topic: Finding nth Term from the Sum of n Terms

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 430/5/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2026: question 28(a)

Hints

Step-by-step solution

Revise the chapter

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