Question

The average of 9 consecutive natural numbers is 25 which is the smallest among them​

Answer 1

Given:

Average of 9 consecutive natural numbers = 25

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To find:

The smallest number.

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Solution:

$\bigstar {\sf {\orange {Let\ the\ first\ number\ be\ x.}}}$

$\bigstar {\sf {\orange {Let\ the\ second\ consecutive\ number\ be\ (x+1).}}}$

$\bigstar {\sf {\orange {Let\ the\ third\ consecutive\ number\ be\ (x+2).}}}$

$\bigstar {\sf {\orange {Let\ the\ fourth\ consecutive\ number\ be\ (x+3).}}}$

$\bigstar {\sf {\orange {Let\ the\ fifth\ consecutive\ number\ be\ (x+4).}}}$

$\bigstar {\sf {\orange {Let\ the\ sixth\ consecutive\ number\ be\ (x+5).}}}$

$\bigstar {\sf {\orange {Let\ the\ seventh\ consecutive\ number\ be\ (x+6).}}}$

$\bigstar {\sf {\orange {Let\ the\ eighth\ consecutive\ number\ be\ (x+7).}}}$

$\bigstar {\sf {\orange {Let\ the\ ninth\ consecutive\ number\ be\ (x+8).}}}$

Now, we know that

$\sf Average = \dfrac{Sum \: of \: all \: the \: observations}{Total \: number \: of \: observations}$

$\sf 25 = \dfrac{x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) + (x + 7) + (x + 8)}{9}$

$\sf 25 = \dfrac{x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 + x + 8}{9}$

$\sf 25= \dfrac{9x + 36}{9}$

$\sf {25 \times 9 = 9x+36}$

$\sf {225 = 9x+36}$

$\sf {225 - 36 = 9x}$

$\sf {189 = 9x}$

$\sf {\dfrac {189}{9} = x}$

$\boxed {\bf {\red {21=x}}}$

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The smallest number:

The first or the smallest number was considered to be x.

So, the smallest number is 21.