MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 26(A)

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section C, question 26(A), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(A) · 3 marks · Short answerArithmetic Progressions

How many terms are there in an A.P. whose first and fifth terms are -14 and 2, respectively and the last term is 62.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

Write the fifth term as $a + 4 d$ and find the common difference.

Hint 2

Now put $a_{n} = a + (n - 1) d$ equal to the last term, 62, and solve for n.

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.

Here $a = - 14$ and $a_{5} = 2$ .
Using $a_{n} = a + (n - 1) d$ : $a_{5} = a + 4 d = 2$ .
1 mark
$- 14 + 4 d = 2$ , so $4 d = 16$ and $d = 4$ .
1 mark
The last term is $a_{n} = 62$ :
$- 14 + (n - 1) (4) = 62$
$(n - 1) \cdot 4 = 76$ , so $n - 1 = 19$ and $n = 20$ .
The A.P. has 20 terms.
1 mark

Answer: 20 terms

Where the marks are

Writes $a + 4 d = 2$ using the fifth term (1 mark)
Finds $d = 4$ (1 mark)
Uses $a_{n} = 62$ to get $n = 20$ (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 30/4/1 (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 26(A)

Hints

Step-by-step solution

Revise the chapter

More questions from Arithmetic Progressions