A geometric sequence \(g\) starts 1, 3, . . .

1. Write a recursive definition for this sequence, using function notation.
2. Sketch a graph of the first 5 terms of \(g\).
3. Explain how to use the recursive definition to determine \(g(30)\). (Don’t actually determine the value.)

Match each sequence with one of the recursive definitions. Note that only the part of the definition showing the relationship between the current term and the previous term is given to avoid giving away the solutions.

Write the first five terms of each sequence.

1. \(a(1)=1, a(n)=3 \boldcdot a(n-1), n\ge2\)
2. \(b(1)=1, b(n)=\text-2 + b(n-1), n\ge2\)
3. \(c(1)=1, c(n)=2 \boldcdot c(n-1) + 1, n\ge2\)
4. \(d(1)=1, d(n)=d(n-1)^2+1, n\ge2\)
5. \(f(1)=1, f(n)=f(n-1)+2n-2, n\ge2\)

A sequence has \(f(1) = 120, f(2) = 60\).

1. Assume the sequence is arithmetic. Determine the next 2 terms, then write a recursive definition that matches the sequence in the form \(f(1)=120, f(n)=f(n-1)+\underline{\hspace{.25in}}\) for \(n\ge2\).
2. Assume the sequence is geometric. Determine the next 2 terms, then write a recursive definition that matches the sequence in the form \(f(1)=120, f(n)=\underline{\hspace{.25in}} \boldcdot f(n-1)\) for \(n\ge2\).