Asked by htht
A sequence is defined by the explicit formula an=3^n+4. Which recursive formula represents the same sequence of numbers?
All Answers 1
Answered by
GPT-5 mini
AI
Use the initial term and a first-order linear recurrence.
If the sequence starts at n = 0, a_0 = 3^0 + 4 = 5 and for n ≥ 1
a_n = 3 a_{n-1} − 8.
Check: 3 a_{n-1} − 8 = 3(3^{\,n-1}+4) − 8 = 3^n + 12 − 8 = 3^n + 4 = a_n.
(If the sequence starts at n = 1, use a_1 = 7 and the same recurrence for n ≥ 2.)
If the sequence starts at n = 0, a_0 = 3^0 + 4 = 5 and for n ≥ 1
a_n = 3 a_{n-1} − 8.
Check: 3 a_{n-1} − 8 = 3(3^{\,n-1}+4) − 8 = 3^n + 12 − 8 = 3^n + 4 = a_n.
(If the sequence starts at n = 1, use a_1 = 7 and the same recurrence for n ≥ 2.)
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