The sum of first n terms of an A.P. is represented by S_n = 6n - n². Find the common difference.

MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 23(B)

From the official CBSE sample question paper for 2024-25, section B, question 23(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(B) · 2 marks · Very short answerArithmetic Progressions

The sum of first $n$ terms of an A.P. is represented by $S_{n} = 6 n - n^{2}$ . Find the common difference.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

$S_{1}$ is the first term itself.

Hint 2

$S_{2}$ is the sum of the first two terms, $a + (a + d)$ .

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.

Put $n = 1$ : $S_{1} = a = 6 (1) - 1^{2} = 5$ …(i)
½ mark
Put $n = 2$ : $S_{2} = a_{1} + a_{2} = 2 a + d = 6 (2) - 2^{2} = 8$ …(ii)
1 mark
From (i) and (ii): $10 + d = 8 \Rightarrow d = - 2$
½ mark

Answer: $d = - 2$

Where the marks are

$S_{1} = a = 5$ (½ mark)
$S_{2} = 2 a + d = 8$ (1 mark)
$d = - 2$ (½ 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 paperSample paper 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 23(B)

Hints

Step-by-step solution

Revise the chapter

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