MathsCBSE Class 10 · Standard · Board exam 2023, set 30/6/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard 2023: question 34(B)

Set in the CBSE Class 10 board exam of 2023, paper 30/6/1, section D, question 34(B), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q34(B) · 5 marks · Long answerArithmetic Progressions

If the sum of first 6 terms of an A.P. is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/6/1.

Hints

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

Hint 1

Write two equations in a and d using $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ .

Hint 2

Subtract the equations to find d, then a, and use them in $S_{10}$ .

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.

$S_{6} = 36 \Rightarrow \frac{6}{2} [2 a + 5 d] = 36$ .
1 mark
$\Rightarrow 2 a + 5 d = 12$ …(1)
1 mark
$S_{16} = 256 \Rightarrow \frac{16}{2} [2 a + 15 d] = 256 \Rightarrow 2 a + 15 d = 32$ …(2)
1 mark
Subtracting (1) from (2): $10 d = 20 \Rightarrow d = 2$ . Then from (1), $2 a = 12 - 10 = 2 \Rightarrow a = 1$ .
1 mark
$S_{10} = \frac{10}{2} [2 (1) + 9 (2)] = 5 \times 20 = 100$ .
1 mark

Answer: $S_{10} = 100$

Where the marks are

Uses the $S_{n}$ formula for $S_{6}$ (1 mark)
Gets 2a + 5d = 12 (1 mark)
Gets 2a + 15d = 32 (1 mark)
Solves to get d = 2, a = 1 (1 mark)
Finds $S_{10} = 100$ (1 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 paper2023 board paper, set 30/6/1 (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 2023: question 34(B)

Hints

Step-by-step solution

Revise the chapter

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