MathsCBSE Class 10 · Standard · Board exam 2024, set 30/2/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 26(b)

Set in the CBSE Class 10 board exam of 2024, paper 30/2/1, section C, question 26(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(b) · 3 marks · Short answerArithmetic Progressions

In an A.P., the sum of three consecutive terms is $24$ and the sum of their squares is $194$ . Find the numbers.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/2/1.

Hints

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

Hint 1

Choose the terms symmetrically as $a - d, a, a + d$ so that $d$ cancels in the sum.

Hint 2

Substitute $a$ in the sum of squares; the cross terms cancel.

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 the three consecutive terms be $a - d, a, a + d$ .
½ mark
Sum: $(a - d) + a + (a + d) = 24 \Rightarrow 3 a = 24 \Rightarrow a = 8$ .
½ mark
Sum of squares: $(8 - d)^{2} + 8^{2} + (8 + d)^{2} = 194 \Rightarrow 192 + 2 d^{2} = 194$ .
1 mark
$\Rightarrow d^{2} = 1 \Rightarrow d = \pm 1$ .
½ mark
Numbers are $7, 8, 9$ (for $d = 1$ ) or $9, 8, 7$ (for $d = - 1$ ).
½ mark

Answer: 7, 8, 9 (or 9, 8, 7)

Where the marks are

Takes terms as $a - d, a, a + d$ (½ mark)
Finds $a = 8$ (½ mark)
Forms the sum-of-squares equation (1 mark)
$d = \pm 1$ (½ mark)
Numbers 7, 8, 9 (½ mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)
Topic: Sum of First n Terms of an AP

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paper2024 board paper, set 30/2/1 (Standard): 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 Standard 2024: question 26(b)

Hints

Step-by-step solution

Revise the chapter

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