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The sum of the first $10$ terms of an AP is $230$ . If the first term is $5$ , what is the common difference?

medium MCQ 3 marks Class 10 · Mathematics · Arithmetic Progressions

2
3
4
5

Answer

4

The correct answer is 4 — Divide by $9$ : $d = 4$ .

Step-by-step solution

Use the sum formula: $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$ .
Substitute $S_{10} = 230$ , $n = 10$ , $a = 5$ :
$230 = \frac{10}{2} [2 \times 5 + (10 - 1) d] = 5 [10 + 9 d]$ .
Divide both sides by $5$ : $46 = 10 + 9 d$ .
Subtract $10$ : $36 = 9 d$ .
Divide by $9$ : $d = 4$ .

Common mistake: Forgetting to divide the total sum by

\frac{n}{2}

before isolating

d

.

Concept tested: sum of n terms

Published 19 August 2026 · How this solution was prepared and checked

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