Write a recursive rule for the sequence

Write an explicit rule for the sequence using your recursive rule.

Ask by Ward Estrada. in the United States

Mar 27,2025

Question

Write a recursive rule for the sequence $$ 5,-20,80,-320,1280, \ldots $$ $$ a_{1}=5, a_{n}=\square $$ Write an explicit rule for the sequence using your recursive rule. $$ a_{n}=\square $$

UpStudy AI · Accepted Answer

1. **Recursive Rule:**

The ratio between consecutive terms is
   $$
   \frac{-20}{5} = -4, \quad \frac{80}{-20} = -4, \quad \frac{-320}{80} = -4, \quad \frac{1280}{-320} = -4.
   $$
   Therefore, the recursive rule is
   $$
   a_{1} = 5, \quad a_{n} = -4a_{n-1} \quad \text{for } n \geq 2.
   $$

2. **Explicit Rule:**

Since the sequence is geometric with the first term $$ 5 $$ and common ratio $$ -4 $$, the explicit rule is
   $$
   a_{n} = 5(-4)^{n-1} \quad \text{for } n \geq 1.
   $$
**Recursive Rule:** - First term: $$ a_{1} = 5 $$ - Each next term: $$ a_{n} = -4 \times a_{n-1} $$ for $$ n \geq 2 $$ **Explicit Rule:** - $$ a_{n} = 5 \times (-4)^{n-1} $$ for $$ n \geq 1 $$

Write a recursive rule for the sequence

Write an explicit rule for the sequence using your recursive rule.

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Write a recursive rule for the sequence Write an explicit rule for the sequence using your recursive rule.