The arithmetic mean of a,a+d,a+2d,…,a+2nd is

a+(a+d)+…+(a+2nd)=(2n+1)a+dn(2n+1)=(2n+1)(a+dn)

The arithmetic mean of a,a+d,a+2d,…,a+2nd is

a+(a+d)+…+(a+2nd)=(2n+1)a+dn(2n+1)=(2n+1)(a+dn)

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The arithmetic mean of $a, a + d, a + 2 d, \dots, a + 2 n d$ is

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$a + (n + 2) d$

$a + (n + 1) d$

none of these

$a + (n - 1) d$

answer is D.

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Detailed Solution

$\begin{array}{l} a + (a + d) + \dots + (a + 2 n d) \\ = (2 n + 1) a + d n (2 n + 1) \\ = (2 n + 1) (a + d n) \end{array}$

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The arithmetic mean of a,a+d,a+2d,…,a+2nd is

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The arithmetic mean of $a, a + d, a + 2 d, \dots, a + 2 n d$ is