MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2026: question 27(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section C, question 27(a), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(a) · 3 marks · Short answerArithmetic Progressions

In an A.P., 15th term exceeds the 8th term by 21. If sum of first 10 terms is 55, then form the A.P.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

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

Hint 1

Write $a_{15}$ and $a_{8}$ in terms of $a$ and $d$ .

Hint 2

The first condition gives $d$ directly.

Hint 3

Use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ with $n = 10$ to find $a$ .

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.

Let first term $= a$ , common difference $= d$ . Given $a_{15} = a_{8} + 21$ : $a + 14 d = a + 7 d + 21$
1 mark
$7 d = 21 \Rightarrow d = 3$
½ mark
$S_{10} = \frac{10}{2} [2 a + (10 - 1) d] \Rightarrow 55 = 5 [2 a + 27]$
½ mark
$11 = 2 a + 27 \Rightarrow 2 a = - 16 \Rightarrow a = - 8$
½ mark
The A.P. is $- 8, - 5, - 2, 1, \dots$
½ mark

Answer: A.P.: $- 8, - 5, - 2, 1, \dots$ ( $a = - 8$ , $d = 3$ )

Where the marks are

Forms $a + 14 d = a + 7 d + 21$ (1 mark)
$d = 3$ (½ mark)
Uses $S_{10} = 55$ correctly (½ mark)
$a = - 8$ (½ mark)
Writes the A.P. (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 30/5/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2026: question 27(a)

Hints

Step-by-step solution

Revise the chapter

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