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B-106.

Wade and Dwayne were working together writing an equation for the sequence $12,36,108,324,\ ...$ Wade wrote $t(n)=4·3^n$ and Dwayne wrote $t(n)=12·3^{n-1}$.

1. Make a table for the first four terms of each of their sequences. What do you notice?

Are there any similarities between the two sequences?
Are there any differences?

2. How do you think Dwayne explained his method of writing the equation to Wade?

The coefficient is the first term of the sequence and the exponent is $n − 1$.

3. For the sequence $10.3,11.5,12.7,\dots,$ Wade wrote $t(n)=9.1+1.2n$ while Dwayne wrote $t(n)=10.3+1.2(n-1)$. Make a table for the first four terms of each of their sequences. Are both forms of the equation correct?

This is similar to part (a).
Are the two sequences similar or different?
What does that tell you about the two forms of the sequence?

4. Dwayne calls his equations the “first term” form. Why do you think he calls them “first term” form? Why does Dwayne subtract one in both situations?

Look at Dwayne's sequence.
Which term is the coefficient?
How would this affect the way he defines his sequence?