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If the sum of the series $54+51+48+$ ________ is 513, then the number of terms are
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Verified Answer
The correct answer is:
$18$
According to condition
$\Rightarrow 513=\frac{n}{2}\{2 \times 54+(n-1)(-3)\}$
$\Rightarrow 1026=n(111-3 n)$ $\Rightarrow 3 n^2-111 n+1026=0$
$\Rightarrow \quad(3 n-57)(n-18)=0$
Hence $n=18$.
$\Rightarrow 513=\frac{n}{2}\{2 \times 54+(n-1)(-3)\}$
$\Rightarrow 1026=n(111-3 n)$ $\Rightarrow 3 n^2-111 n+1026=0$
$\Rightarrow \quad(3 n-57)(n-18)=0$
Hence $n=18$.
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