6. Recursively Defined Sequences
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Check for a common ratio.
No, see solution.
Let's start by checking for a common ratio in the given sequence.
We see that there is common ratio of - 1, so it is a geometric sequence with first term a_1=- 5. Since it is geometric, we can represent it with a recursive rule. Let's write the recursive equation. a_n= r* a_(n-1) ⇕ a_n= - 1* a_(n-1) The recursive rule for the sequence is a_1=- 5, a_n=- 1* a_(n-1). Recursive Rule: a_1=- 5, a_n=- 1* a_(n-1) Therefore, our friend's claim is not correct.