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Here is the recursive definition of a sequence: \(f(1) = 10, f(n) = f(n-1) - 1.5\) for \(n\ge2\).
An arithmetic sequence \(k\) starts 12, 6, . . .
An arithmetic sequence \(a\) begins 11, 7, . . .
A geometric sequence \(g\) starts 80, 40, . . .
Match each recursive definition with one of the sequences.
\(h(1)=1, h(n)=2 \boldcdot h(n-1) + 1\) for \(n\ge2\)
\(p(1) = 1, p(n) = 2 \boldcdot p(n-1)\) for \(n\ge2\)
\(a(1) = 80, a(n) = \frac 1 2 \boldcdot a(n-1)\) for \(n\ge2\)
80, 40, 20, 10, 5
1, 2, 4, 8, 16
1, 3, 7, 15, 31
For each sequence, decide whether it could be arithmetic, geometric, or neither.
For each sequence that is neither arithmetic nor geometric, how can you change a single number to make it an arithmetic sequence? A geometric sequence?