If $T_{n} = n^{2} + 1,$ find $S_{2}$

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Solution

We know $S_{2} = T_{1} + T_{2}$
$T_{n} = n^{2} + 1$
$T_{1} = 1^{2} + 1 = 1 + 1 = 2$
$T_{2} = 2^{2} + 1 = 4 + 1 = 5$
$∴ S_{2} = T_{1} + T_{2}$
$S_{2} = 2 + 5$
$S_{2} = 7$

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