The average of odd numbers up to 100 is? | vedclass

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(B) The odd numbers up to $100$ are $1, 3, 5, \dots, 99$.This is an arithmetic progression where the first term $a = 1$, the last term $l = 99$, and t

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(B) The odd numbers up to $100$ are $1, 3, 5, \dots, 99$.This is an arithmetic progression where the first term $a = 1$, the last term $l = 99$, and the common difference $d = 2$.The number of terms $n$ can be calculated as $l = a + (n - 1)d$, so $99 = 1 + (n - 1)2$, which gives $98 = 2(n - 1)$, so $n - 1 = 49$, and $n = 50$.The average of an arithmetic progression is given by the formula $	ext{Average} = \frac{	ext{First term} + 	ext{Last term}}{2}$.$	ext{Average} = \frac{1 + 99}{2} = \frac{100}{2} = 50$.

The average of odd numbers up to $100$ is?

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