MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2023: question 33

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section D, question 33, for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33 · 5 marks · Long answerArithmetic Progressions

The first term of an A.P. is 22, the last term is $- 6$ and the sum of all the terms is 64. Find the number of terms of the A.P. Also, find the common difference.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Since the first and last terms are known, use the sum formula with the last term.

Hint 2

After finding n, use $a_{n} = a + (n - 1) d$ with $a_{n} = - 6$ to get d.

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.

Given $a = 22$ , last term $l = a_{n} = - 6$ , $S_{n} = 64$ . Using $S_{n} = \frac{n}{2} (a + l)$ : $64 = \frac{n}{2} [22 + (- 6)] = \frac{n}{2} \times 16$
2 marks
$8 n = 64 \Rightarrow n = 8$ . So there are 8 terms.
1 mark
Using $a_{n} = a + (n - 1) d$ : $- 6 = 22 + (8 - 1) d \Rightarrow 7 d = - 28$
1 mark
$d = - 4$
1 mark

Answer: n = 8, d = −4

Where the marks are

Uses $S_{n} = \frac{n}{2} (a + l)$ correctly: $\frac{n}{2} (22 - 6) = 64$ (2 marks)
n = 8 (1 mark)
Uses $a_{n} = a + (n - 1) d$ : 22 + 7d = −6 (1 mark)
d = −4 (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 430/6/1 (Basic): 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 Basic 2023: question 33

Hints

Step-by-step solution

Revise the chapter

More questions from Arithmetic Progressions