If $T_{n} = 2 n^{2} + 5$ , find (i) $T_{3}$ and (ii) $T_{10}$

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Solution

The given sequence is $t_{n} = 2 n^{2} + 5$ .

The third term $t_{3}$ can be determined by substituting $n = 3$ in the sequence $t_{n} = 2 n^{2} + 5$ as follows:

$t_{3} = 2 (3)^{2} + 5 = (2 \times 9) + 5 = 18 + 5 = 23$

The tenth term $t_{10}$ can be determined by substituting $n = 10$ in the sequence $t_{n} = 2 n^{2} + 5$ as follows:

$t_{10} = 2 (10)^{2} + 5 = (2 \times 100) + 5 = 200 + 5 = 205$

Hence, $t_{3} = 23$ and $t_{10} = 205$

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