MathsCBSE Class 10 · Basic · Sample paper, session 2024-25 · 2 marks · Very short answer

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 23(A)

From the official CBSE sample question paper for 2024-25, section B, question 23(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(A) · 2 marks · Very short answerArithmetic Progressions

The sum of the first 12 terms of an A.P. is 900. If its first term is 20 then find the common difference and $1 2^{t h}$ term.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ with $n = 12$ .

Hint 2

Once you know $d$ , use $a_{n} = a + (n - 1) d$ .

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.

Using $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ with $n = 12$ , $a = 20$ :
$\frac{12}{2} [2 \times 20 + 11 d] = 900$
½ mark
$6 (40 + 11 d) = 900 \Rightarrow 40 + 11 d = 150 \Rightarrow 11 d = 110 \Rightarrow d = 10$
1 mark
$a_{12} = a + 11 d = 20 + 11 \times 10 = 130$
½ mark

Answer: $d = 10$ , $a_{12} = 130$

Where the marks are

Correct substitution in the $S_{n}$ formula (½ mark)
$d = 10$ (1 mark)
$a_{12} = 130$ (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 paperSample paper 2024-25 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2024-25: question 23(A)

Hints

Step-by-step solution

Revise the chapter

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