Wade and Dwayne were working together writing an equation for the sequence 12, 36, 108, 324, … Wade wrote t(n) = 4 · 3n and Dwayne wrote t(n) = 12 · 3n−1. Homework Help ✎
Make a table for the first four terms of each of their sequences. What do you notice?
How do you think Dwayne explained his method of writing the equation to Wade?
For the sequence 10.3, 11.5, 12.7, …, 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?
Read the Math Notes box about standard form of a sequence in this lesson. Dwayne’s equations are based on the first term of each sequence, not on the zeroth term. Why does Dwayne subtract one in both situations?
Are there any similarities between the two sequences?
Are there any differences?
The coefficient is the first term of the sequence and the exponent is n −1.
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?
Look at Dwayne's sequence.
Which term is the coefficient?
How would this effect the way he defines his sequence?