MathsCBSE Class 10 · Basic · Board exam 2023, set 430/4/1 · 5 marks · Long answer

CBSE Class 10 Mathematics Basic 2023: question 33(A)

Set in the CBSE Class 10 board exam of 2023, paper 430/4/1, section D, question 33(A), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q33(A) · 5 marks · Long answerArithmetic Progressions

Find the sum of first $25$ terms of the A.P. whose $n^{t h}$ term is given by $a_{n} = 5 + 6 n$ . Also, find the ratio of $2 0^{t h}$ term to $4 5^{t h}$ term.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/4/1.

Hints

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

Hint 1

Put n = 1 and n = 2 in $a_{n}$ to get the first term and common difference.

Hint 2

Use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ ; for the ratio, substitute n = 20 and n = 45 directly in $a_{n}$ .

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.

$a_{1} = 5 + 6 (1) = 11$
½ mark
$a_{2} = 5 + 6 (2) = 17$
½ mark
$d = a_{2} - a_{1} = 17 - 11 = 6$
½ mark
$S_{n} = \frac{n}{2} [2 a + (n - 1) d] \Rightarrow S_{25} = \frac{25}{2} [2 (11) + 24 (6)] = \frac{25}{2} [22 + 144]$
1 mark
$S_{25} = \frac{25}{2} \times 166 = 2075$
½ mark
$a_{20} = 5 + 6 (20) = 125$ and $a_{45} = 5 + 6 (45) = 275$
1 mark
$\frac{a _{20}}{a _{45}} = \frac{125}{275} = \frac{5}{11}$ , so the ratio is $5 : 11$ .
1 mark

Answer: S₂₅ = 2075; a₂₀ : a₄₅ = 5 : 11

Where the marks are

$a_{1} = 11$ (½ mark)
$a_{2} = 17$ (½ mark)
$d = 6$ (½ mark)
Correct substitution in $S_{n}$ formula (1 mark)
$S_{25} = 2075$ (½ mark)
Finds $a_{20} = 125$ and $a_{45} = 275$ (1 mark)
Ratio $5 : 11$ (1 mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)
Topic: nth Term of an AP

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 430/4/1 (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(A)

Hints

Step-by-step solution

Revise the chapter

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