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

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

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, 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

The ratio of the 10th term to its 30th term of an A.P. is 1 : 3 and the sum of its first six terms is 42. Find the first term and the common difference of A.P.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Write the 10th and 30th terms using $a_{n} = a + (n - 1) d$ .

Hint 2

Cross-multiply the ratio to find a relation between a and d. Then use $S_{6} = 42$ .

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 first term be $a$ and the common difference be $d$ . Then $a_{10} = a + 9 d$ and $a_{30} = a + 29 d$ , so $\frac{a + 9 d}{a + 29 d} = \frac{1}{3}$ .
½ mark
$3 a + 27 d = a + 29 d \Rightarrow 2 a = 2 d \Rightarrow a = d$ ...(i)
½ mark
$S_{6} = \frac{6}{2} (2 a + 5 d) = 42$
½ mark
$\Rightarrow 2 a + 5 d = 14$ ...(ii)
½ mark
Put $d = a$ in (ii): $7 a = 14 \Rightarrow a = 2$ , so $d = 2$ .
1 mark

Answer: First term a = 2, common difference d = 2

Where the marks are

Writes $\frac{a + 9 d}{a + 29 d} = \frac{1}{3}$ (½ mark)
Simplifies to $a = d$ (½ mark)
Writes $S_{6} = \frac{6}{2} (2 a + 5 d) = 42$ (½ mark)
Simplifies to $2 a + 5 d = 14$ (½ mark)
Gets $a = 2$ and $d = 2$ (½ + ½ marks)

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 paper2024 board paper, set 30/3/1 (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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