Create an explicit equation for each recursively defined sequence below:
1 answer:
Part A
This is an arithmetic sequence with starting term a(1) = 17 and common difference d = -7.
a(n) = a(1) + d(n-1)
a(n) = 17 + (-7)(n-1)
a(n) = 17-7(n-1)
a(n) = 17-7n+7
<h3>a(n) = -7n+24 is the final answer</h3>
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Part B
We have a geometric sequence here because we multiply by the same quantity (5) each time. This makes the common ratio be r = 5.
The starting term is t1 = 3
The nth term of this geometric sequence can be expressed as...
t(n) = t1*(r)^(n-1)
<h3>t(n) = 3*(5)^(n-1) is the final answer</h3>
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