Writing the Terms of a Sequence Defined by a Piecewise Explicit Formula

Write the first six terms of the sequence.

a_{n} = {\begin{array}{l} n^{2} & if n is not divisible by 3 \\ \frac{n}{3} & if n is divisible by 3 \end{array}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Substitute $n = 1, n = 2,$ and so on in the appropriate formula. Use $n^{2}$ when $n$ is not a multiple of 3. Use $\frac{n}{3}$ when $n$ is a multiple of 3.
$\begin{array}{l} a_{1} = 1^{2} = 1 \begin{matrix} \end{matrix} & 1 is not a multiple of 3 . Use n^{2} . \\ a_{2} = 2^{2} = 4 & 2 is not a multiple of 3 . Use n^{2} . \\ a_{3} = \frac{3}{3} = 1 & 3 is a multiple of 3 . Use \frac{n}{3} . \\ a_{4} = 4^{2} = 16 & 4 is not a multiple of 3 . Use n^{2} . \\ a_{5} = 5^{2} = 25 & 5 is not a multiple of 3 . Use n^{2} . \\ a_{6} = \frac{6}{3} = 2 & 6 is a multiple of 3 . Use \frac{n}{3} . \end{array}$
The first six terms are ${1, 4,} .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write the first six terms of the sequence.

a_{n} = {\begin{array}{l} 2 n^{3} & if n is odd \\ \frac{5 n}{2} & if n is even \end{array}

How did it go?