Mathematics — Standard (041) — CBSE Class 10 board question

Given: $S_n = n(4n + 1) = 4n^2 + n$

First term: $a_1 = S_1 = 4(1)^2 + 1 = 5$

Second term: $S_2 = 4(4) + 2 = 18$, so $a_2 = S_2 - S_1 = 18 - 5 = 13$

Third term: $S_3 = 4(9) + 3 = 39$, so $a_3 = S_3 - S_2 = 39 - 18 = 21$

Common difference $d = 13 - 5 = 8$

∴ The AP is 5, 13, 21, 29, …

Source: Chapter 5, Arithmetic Progressions

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• Examiners expect you to find $a_1 = S_1$, then use $a_n = S_n - S_{n-1}$ for $n \geq 2$ to get at least two more terms.
• Always verify $d$ is constant to confirm it's an AP.
• Writing the AP at the end is essential for full marks — don't leave it implied.