If $T_{n} = n^{2} + 4$ and $T_{n} = 200$ , find the value of $n$ .

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Solution

The given sequence is $T_{n} = n^{2} + 4$ where $T_{n} = 200$ .

Substitute $T_{n} = 200$ in the sequence $T_{n} = n^{2} + 4$ as follows:

$T_{n} = n^{2} + 4 \Rightarrow 200 = n^{2} + 4 \Rightarrow n^{2} = 200 - 4 = 196 \Rightarrow n^{2} = 196 \Rightarrow n = \sqrt{196} = 14$

Hence, $n = 14$

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