Skip to content

If p^th term of an A.P. is q… (Class 10 Maths 2023, Q27)

questionbuddy.in/q/cbse-10-maths-2023-30-5-1-q27-term-term-term

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 27

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerArithmetic Progressions

If term of an A.P. is q and term is p, then prove that its term is .

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

Write the two given terms using .

Hint 2

Subtract the two equations to find d first.

Hint 3

Put d back to find a, then write the general term.

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.

  1. Let the first term be and common difference . Given : ……(i)

    ½ mark

  2. Given : ……(ii)

    ½ mark

  3. Subtracting (ii) from (i): . Since , .

    ½ mark

  4. Substituting in (i): .

    ½ mark

  5. . Hence proved.

    1 mark

Answer: d = −1, a = p + q − 1, so aₙ = p + q − n (proved).

Where the marks are

  • Writes a + (p − 1)d = q (½ mark)
  • Writes a + (q − 1)d = p (½ mark)
  • Solves to get d = −1 (½ mark)
  • Finds a = p + q − 1 (½ mark)
  • Obtains aₙ = p + q − n (1 mark)

Revise the chapter

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 30/5/1 (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.