MathsCBSE Class 10 · Standard · Board exam 2024, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 27(a)

Set in the CBSE Class 10 board exam of 2024, 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

If the sum of the first 14 terms of an A.P. is 1050 and the first term is 10, then find the 20th term and the $n^{t h}$ term.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/5/1.

Hints

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

Hint 1

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

Hint 2

Once d is known, use $a_{n} = a + (n - 1) d$ for both terms.

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.

$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ with $a = 10$ , $n = 14$ : $\frac{14}{2} (20 + 13 d) = 1050$
1 mark
$20 + 13 d = 150 \Rightarrow 13 d = 130 \Rightarrow d = 10$
1 mark
$a_{20} = a + 19 d = 10 + 19 \times 10 = 200$
½ mark
$a_{n} = a + (n - 1) d = 10 + (n - 1) 10 = 10 n$
½ mark

Answer: $a_{20} = 200$ , $a_{n} = 10 n$

Where the marks are

Forms $\frac{14}{2} (20 + 13 d) = 1050$ (1 mark)
Finds $d = 10$ (1 mark)
$a_{20} = 200$ (½ mark)
$a_{n} = 10 n$ (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 paper2024 board paper, set 30/5/1 (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 27(a)

Hints

Step-by-step solution

Revise the chapter

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