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A-114.

Consider the following sequences as you complete parts (a) through (c) below.

Sequence 1
$2$, $6$, …

Sequence 2
$24$, $12$, …

Sequence 3
$1$, $5$, …

1. Assuming that the sequences above are arithmetic with $t(1)$ as the first term, find the next four terms for each sequence. For each sequence, write an explanation of what you did to get the next term and write an equation for $t(n)$.

Add $4$ to each term to get the next.

The next $4$ terms are $10$, $14$, $18$, $22$.
$t(n) = 4n − 2$

2. Would your terms be different if the sequences were geometric? Find the next four terms for each sequence if they are geometric. For each sequence, write an explanation of what you did to get the next term and write an equation for $t(n)$.

Multiply each term by $3$ to get the next term.

The next $4$ terms are $18$, $54$, $162$, $486$.

$t(n)=\frac{2}{3}\left(3\right)^n$

3. Create a totally different type of sequence for each pair of values shown above, based on your own equation. Write your equation clearly (using words or algebra) so that someone else will be able to find the next three terms that you want.

Use your equation to generate a sequence. Does your equation generate the sequence you created?