Math Problem Statement
A sequence is defined recursively by the given formulas. Find the first five terms of the sequence: a_n = a_(n-1)/5 and a_1 = -20.
Solution
The given problem describes a sequence defined recursively with the formulas:
We are tasked to find the first five terms of the sequence. Let's compute them step by step:
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Final Result:
a_1 &= -20, \\ a_2 &= -4, \\ a_3 &= -0.8, \\ a_4 &= -0.16, \\ a_5 &= -0.032. \end{aligned}$$ Would you like a detailed explanation of the steps? Let me know if you have questions! --- ### Related Questions: 1. What is the general form for this sequence if we need a formula for $$a_n$$? 2. How can we verify convergence of this sequence? 3. What is the sum of the first $$n$$ terms of this sequence? 4. How does the value of $$a_1$$ influence the behavior of the sequence? 5. Can this sequence be represented as a geometric series? **Tip:** Always check recursive steps carefully, as even small errors can propagate through calculations!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Sequences and Series
Recursive Formulas
Arithmetic Operations
Formulas
a_n = a_(n-1)/5
Theorems
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Suitable Grade Level
Grades 9-11