If the sum of the first n terms of an A.P be $3n^2 + n$ and its common difference is 6, then its first term is

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Accepted Answer

## Model Answer $S_1 = 3(1)^2 + 1 = 4$. Since $S_1 = a_1$, the first term is **4**. **(D) 4** ## Explanation The first term of any AP equals $S_1$ (sum of first 1 term). Substitute $n = 1$ in $S_n = 3n^2 + n$: $S_1 = 3 + 1 = 4$. You can verify: $a_2 = S_2 - S_1 = (12+2)-(3+1) = 10$, and $a_2 - a_1 = 10 - 4 = 6$ ✓ (matches given $d = 6$).

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