Question

the average of three consecutive natural numbers are 15. find the value of smallest number

Answer 1

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Given,
Average of three consecutive Natural Numbers = 15

$\underline{\large{\textbf{Step-1}}}$
Note the No. of Observations used in Calculating Average

Here,
Observations are Consecutive Natural Numbers

No. of Observations = 3

$\underline{\large{\textbf{Step-2}}}$
Find the Sum of all Observations

$Average\: of\: Observations = \frac{Sum\: of\: all\: Observations}{No.\: of\: Observations}$

$\implies Sum\: of\: all\: Observations = Average\: of\: observations \times No.\: of\: Observations$

$\implies Sum\: of\: all\: Observations = 15 \times 3$

$\implies Sum\: of\: all\: Observations = 45$ ---------[1]

$\underline{\large{\textbf{Step-3}}}$
Find all the Observations

Let the smallest No. be x
The other numbers are x+1 , x+2
(Given that the Observations are consecutive Natural numbers)

Using [1]
$\implies x+(x+1)+(x+2) = 45$

$\implies 3x+3= 45$

$\implies 3x = 45 - 3$

$\implies 3x = 42$

$\implies x = 14$

$\therefore$
The Smallest Number = 14

$\underline{\textbf{Verification}}$:

Sum of observations = 14 + 15 + 16 = 45

Average of Observations = $\frac{45}{3}$= 15 ✓

Satisfies the data provided

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