If the $n^{t h}$ term of an AP is given by the expression $2 n + 1$ , then its common difference is:

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Solution

The correct option is B 2
Given $n^{t h}$ term $= 2 n + 1$
Substitute $n = 1$ to get the first term,
$\Rightarrow 1^{s t}$ term $= (2 \times 1) + 1$
$= 2 + 1 = 3$
Substitute $n = 2$ to get the second term
$\Rightarrow 2^{n d}$ term $= (2 \times 2) + 1$
$= 4 + 1$
Thus, $2^{n d}$ term $= 5$
Since, common difference $= 2^{n d}$ term $- 1^{s t}$ term
$= 5 - 3$
$= 2$
Therefore, the common difference is $2$

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