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If S_n = n^2 + 3 n, then first term and common difference are
Aa = 2 and d = 4 by check
Ba = 3 and d = 4 by check
Ca = 5 and d = 3 by check
Da = 4 and d = 2
Answer & Solution
Correct answer: D. a = 4 and d = 2
1. a_1 = S_1 = 1 + 3 = 4.
2. S_2 = 4 + 6 = 10, so a_2 = S_2 - S_1 = 10 - 4 = 6.
3. d = a_2 - a_1 = 6 - 4 = 2.
4. So a = 4 and d = 2.
_Source: Selina Concise Mathematics Class 10, Ch on Arithmetic Progression (Mistral OCR'd PDF), section on relation between S_n and a_n_
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