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Mathematics — CBSE Class 10 board question

Q1. [1]
The common difference of the A.P. whose $n$th term is given by $a_n = 3n + 7$, is :
  1. (a) $7$
  2. (b) $3$
  3. (c) $3n$
  4. (d) $1$
Previously asked in CBSE board exam
2023 30/5/1 Q3
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer

(b) 3

$a_n = 3n + 7$, so $d = a_{n+1} - a_n = [3(n+1)+7] - [3n+7] = 3$.

Explanation

The common difference is found by subtracting the $k$th term from the $(k+1)$th term. Since $a_n = 3n+7$ is linear in $n$, the coefficient of $n$ (i.e., 3) directly gives the common difference. The constant 7 is part of the first term, not $d$.

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