MathsCBSE Class 10 · Standard · Board exam 2024, set 30/3/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2024: question 26(a)

Set in the CBSE Class 10 board exam of 2024, paper 30/3/1, 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

If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of its first 20 terms.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/3/1.

Hints

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

Hint 1

Apply the sum formula $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ twice.

Hint 2

You get two linear equations in a and d. Solve them, then find $S_{20}$ .

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.

Let the first term be $a$ and the common difference be $d$ . Use $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ . Then $S_{7} = \frac{7}{2} (2 a + 6 d) = 49 \Rightarrow a + 3 d = 7$ ...(i)
½ mark
$S_{17} = \frac{17}{2} (2 a + 16 d) = 289 \Rightarrow a + 8 d = 17$ ...(ii)
½ mark
Subtract (i) from (ii): $5 d = 10 \Rightarrow d = 2$ . Then $a = 7 - 6 = 1$ .
1 mark
$S_{20} = \frac{20}{2} [2 (1) + 19 (2)] = 10 \times 40$
½ mark
$= 400$
½ mark

Answer: S₂₀ = 400

Where the marks are

Forms $a + 3 d = 7$ from $S_{7}$ (½ mark)
Forms $a + 8 d = 17$ from $S_{17}$ (½ mark)
Solves to get $a = 1$ , $d = 2$ (1 mark)
Substitutes correctly in the formula for $S_{20}$ (½ mark)
Gets $S_{20} = 400$ (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 paper2024 board paper, set 30/3/1 (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 2024: question 26(a)

Hints

Step-by-step solution

Revise the chapter

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