Question

what is the average of first 93 natural numbers?​

Answer 1

$\huge\sf\orange{Answer :}$

$\boxed{ Average \: = \: 47 }$

$\huge\sf\purple{Explanation :}$

First 93 natural numbers = 1, 2, 3, ....... ,93

They are in an AP, with

First term (a) = 1

Common Difference (d) = 1

No. of terms (n) = 93

$\: \:$

Sum of first 'n' terms of an AP =

$\frac{n}{2} [2a + (n - 1)d]$

OR,

$\frac{n}{2} (a + l)$

where, l is the last term of the AP.

$\:  \:  \:$

From Formula 1 :

$\frac{93} {2} \times [2 \times 1 + (93 - 1)1]$

➣ $\frac{93}{2} \times (2 + 92)$

➣ $\frac{93}{2} \times 94$

➣ $93 \times 47$

➣ $4371$

$\: \: \:$

From Formula 2 :

$\frac{93}{2} \times (1 + 93)$

➣ $\frac{93}{2} \times 94$

➣ $93 \times 47$

➣ $4371$

$\: \: \: \:$

So, 4371 is the sum of first 93 natural numbers.

To find the average, we know

Average = $\frac{sum \: of \: observations}{no. \: of \: observations}$

➣ $\frac{4371}{93}$

➣ $47$