# The sum of three consecutive odd numbers is $147$.Find the numbers.

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Hint: Let the three consecutive odd numbers be $n,n + 2,n + 4$ using these terms find the number.

Given sum of three consecutive odd numbers = $147$

Let the three consecutive odd numbers be $n,n + 2,n + 4$

By using the condition we can write

$

\Rightarrow n + n + 2 + n + 4 = 147 \\

\Rightarrow 3n + 6 = 147 \\

\Rightarrow 3n = 147 - 6 \\

\Rightarrow 3n = 141 \\

\Rightarrow n = \dfrac{{141}}{3} \\

\Rightarrow n = 47 \\

$

Here we got n value as $47$, substitute the value in three consecutive odd number

$

\Rightarrow n = 47 \\

\Rightarrow n + 2 = 47 + 2 = 49 \\

\Rightarrow n + 4 = 47 + 4 = 51 \\

$

Therefore the three consecutive odd number are $47,49,51$

NOTE: Do not forget to substitute the n value in three consecutive odd number

which are considered for the solution.

Given sum of three consecutive odd numbers = $147$

Let the three consecutive odd numbers be $n,n + 2,n + 4$

By using the condition we can write

$

\Rightarrow n + n + 2 + n + 4 = 147 \\

\Rightarrow 3n + 6 = 147 \\

\Rightarrow 3n = 147 - 6 \\

\Rightarrow 3n = 141 \\

\Rightarrow n = \dfrac{{141}}{3} \\

\Rightarrow n = 47 \\

$

Here we got n value as $47$, substitute the value in three consecutive odd number

$

\Rightarrow n = 47 \\

\Rightarrow n + 2 = 47 + 2 = 49 \\

\Rightarrow n + 4 = 47 + 4 = 51 \\

$

Therefore the three consecutive odd number are $47,49,51$

NOTE: Do not forget to substitute the n value in three consecutive odd number

which are considered for the solution.

Last updated date: 21st Sep 2023

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