The sum S of first n natural numbers is given by the formula S=2n(n+1).If S=231, find n

S=2n(n+1)⇒231=2n(n+1)⇒n2+n−462=0⇒n2+22n−21n−462=0⇒n(n+22)−21(n+22)=0⇒(n+22)(n−21)=0⇒n=−22 or n=21∴n=21 as n=−22 is not a natural number.

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The sum S of first n natural numbers is given by the formula S

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The sum $S$ of first $n$ natural numbers is given by the formula $S = \frac{n ( n + 1 )}{2}$ .If $S = 231,$ find $n$

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Noah Discussed

The sum

S

of first

n

natural numbers is given by the formula

S = \frac{n ( n + 1 )}{2}

.If

S = 231,

find

n

14 mins ago

Discuss this question LIVE

14 mins ago

S = \frac{n ( n + 1 )}{2}

\Rightarrow 231 = \frac{n ( n + 1 )}{2}

\Rightarrow n^{2} + n - 462 = 0

\Rightarrow n^{2} + 22 n - 21 n - 462 = 0

\Rightarrow n (n + 22) - 21 (n + 22) = 0

\Rightarrow (n + 22) (n - 21) = 0

\Rightarrow n = - 22

n = 21

∴ n = 21

n = - 22

is not a natural number.

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Question Text	The sum $S$ of first $n$ natural numbers is given by the formula $S = \frac{n ( n + 1 )}{2}$ .If $S = 231,$ find $n$
Answer Type	Text solution:1
Upvotes	150