Write the first three terms of the sequence $a_{n} = 3 n^{2} - 2$ .

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Solution

Find the first three terms of the sequence $a_{n} = 3 n^{2} - 2$ by substituting $n = 1, 2, 3$ :
$\begin{array}{rcl} \Rightarrow & a_{1} = 3 \times 1^{2} - 2 \\ = & 1 \end{array}$
$\begin{array}{rcl} \Rightarrow & a_{2} = 3 \times 2^{2} - 2 \\ = & 10 \end{array}$
$\begin{array}{rcl} \Rightarrow & a_{3} = 3 \times 3^{2} - 2 \\ = & 25 \end{array}$
The first three terms of the sequence $a_{n} = 3 n^{2} - 2$ is $1, 10, 25$ .

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