The arithmetic mean of the set of variables $a, a + d, a + 2 d, a + 3 d . . . a + 2 n d$ is ________.

a + n d

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a - n d

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a n + d

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a d + n

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Solution

The correct option is A $a + n d$
$a, a + d, . . . . . . a + 2 n d$ is an AP with first term as $a$ , common difference as $d$ and $(2 n + 1)$ terms
Sum of the AP $=$ $\frac{2 n + 1}{2} (2 a + 2 n d)$
Mean of the AP $=$ $\frac{\frac{2 n + 1}{2} (2 a + 2 n d)}{2 n + 1}$ $=$ $a + n d$

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The arithmetic mean of the set of variables a,a+d,a+2d,a+3d...a+2nd is ________.

The correct option is A a+nda,a+d,......a+2nd is an AP with first term as a, common difference as d and (2n+1) termsSum of the AP = 2n+12(2a+2nd)Mean of the AP = 2n+12(2a+2nd)2n+1 = a+nd

The arithmetic mean of the set of variables $a, a + d, a + 2 d, a + 3 d . . . a + 2 n d$ is ________.

The correct option is A $a + n d$
$a, a + d, . . . . . . a + 2 n d$ is an AP with first term as $a$ , common difference as $d$ and $(2 n + 1)$ terms
Sum of the AP $=$ $\frac{2 n + 1}{2} (2 a + 2 n d)$
Mean of the AP $=$ $\frac{\frac{2 n + 1}{2} (2 a + 2 n d)}{2 n + 1}$ $=$ $a + n d$