Question

x is nth term of the given A.P. a_n = x find x .

Answer 1

Suppose x is nth term of the given A.P.

\[a_n = x\]
\[\text{ Here,}  a = - 4, d = 3 . \]
\[\text{ It is given that, }  S_n = 437 . \]
\[ \Rightarrow \frac{n}{2}\left[ 2\left( - 4 \right) + \left( n - 1 \right)3 \right] = 437\]
\[ \Rightarrow 3 n^2 - 11n - 874 = 0\]
\[ \Rightarrow 3 n^2 - 57n + 46n - 874 = 0\]
\[ \Rightarrow 3n\left( n - 19 \right) + 46\left( n - 19 \right) = 0\]
\[ \Rightarrow n = - \frac{46}{3}, 19\]
\[\text{ Since, n cannot be in fraction so}  n = 19 . \]
\[\text{ Now } , a_n = x\]
\[ \Rightarrow \left( - 4 \right) + \left( 19 - 1 \right)3 = x\]
\[ \Rightarrow - 4 + 54 = x\]
\[ \Rightarrow x = 50\]