Question

What is the mean of first 75 odd numbers​

Answer 1

Answer:

the first odd no.means

odd no. is

1,3,5, then

a=1

d=2

the sum of odd no.

using AP formual of sum

s=n/2 (2a+(n-1)d)

s=n/2 (2×1+(n-1)(2)

s=n/2 (2+2n-2)

s=n/2 (2n)

s=n^2

so,

sum of odd no. is n^2

ATQ

total no. is 75

mean =total no. of sum/given no.

mean =n^2/75

mean=75×75/75

mean =75

so,

the first 75 odd no. is 75

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Answer 2

Answer:

75

Step-by-step explanation:

We know that odd numbers are of the form 2k+1; k ∈ N.

Hence, odd numbers forms an AP whose first term(a) is 1 and common difference (d) is 2.

Formula Used:

$1) \,\,\,S_n = \frac{n}{2} [2a+(n-1)d]\\\\2)\,\,\, \mu = \frac{x_1 +x_2 +x_3 +........x_n}{n}$

Where,

1. $S_n$ denotes the sum of the AP having a as the first term and d as common difference.

2. $\mu$ denotes the mean of n numbers denoted by $x_1,x_2,.......x_n$.

Generalization:

So, mean of the first n odd numbers will be given by,

$\mu = \frac{\frac{n}{2}[2(1)+(n-1)*2] }{n} \\\implies \mu = n$

⇒  Mean of first 75 odd numbers​ will be 75 itself.

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