If the sum of first n terms of an A.P. is given by S_n = n/2(2n + 8). Then, find its first term and common difference. Hence, find its 15^th term.

MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 27(b)

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section C, question 27(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27(b) · 3 marks · Short answerArithmetic Progressions

If the sum of first $n$ terms of an A.P. is given by $S_{n} = \frac{n}{2} (2 n + 8)$ . Then, find its first term and common difference. Hence, find its 15 $^{th}$ term.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

Hints

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

Hint 1

The sum of the first term alone is $S_{1}$ .

Hint 2

Find $S_{2}$ ; then $a_{2} = S_{2} - S_{1}$ .

Hint 3

Use $a_{n} = a + (n - 1) d$ with $n = 15$ .

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.

$S_{n} = \frac{n}{2} (2 n + 8) = n (n + 4)$ . First term $a = S_{1} = 1 \times 5 = 5$
½ mark
$S_{2} = 2 \times 6 = 12$
½ mark
$a_{2} = S_{2} - S_{1} = 12 - 5 = 7$ , so $d = a_{2} - a_{1} = 7 - 5 = 2$
1 mark
$a_{15} = a + 14 d = 5 + 14 \times 2 = 33$
1 mark

Answer: $a = 5$ , $d = 2$ , $a_{15} = 33$

Where the marks are

$S_{1} = a = 5$ (½ mark)
$S_{2} = 12$ (½ mark)
$d = 2$ (1 mark)
$a_{15} = 33$ (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 paper2025 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 27(b)

Hints

Step-by-step solution

Revise the chapter

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