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

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

Set in the CBSE Class 10 board exam of 2024, paper 30/5/1, section C, question 27(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(b) · 3 marks · Short answerArithmetic Progressions

The first term of an A.P. is 5, the last term is 45 and the sum of all the terms is 400. Find the number of terms and the common difference of the A.P.

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

When first and last terms are known, the sum is $\frac{n}{2} (a + l)$ .

Hint 2

After finding n, use $a_{n} = a + (n - 1) d = 45$ .

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.

$a = 5$ , $l = a_{n} = 45$ , $S_{n} = 400$ . Using $S_{n} = \frac{n}{2} (a + l)$ : $\frac{n}{2} (5 + 45) = 400$
1 mark
$25 n = 400 \Rightarrow n = 16$
1 mark
$a_{16} = a + 15 d$ : $5 + 15 d = 45$
½ mark
$15 d = 40 \Rightarrow d = \frac{40}{15} = \frac{8}{3}$
½ mark

Answer: n = 16, d = 8/3

Where the marks are

Uses $S_{n} = \frac{n}{2} (a + l)$ correctly (1 mark)
n = 16 (1 mark)
Forms $5 + 15 d = 45$ (½ mark)
d = 8/3 (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(b)

Hints

Step-by-step solution

Revise the chapter

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