To find $a_2$, $a_3$, $a_4$, and $a_5$ given the recursive formula:

$a_1 = 55$ $a_n = -\frac{1}{5} a_{n-1}$

We will calculate each term step by step.

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Step 1: Find $a_2$

$a_2 = -\frac{1}{5} a_1 = -\frac{1}{5} \times 55 = -11$

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Step 2: Find $a_3$

$a_3 = -\frac{1}{5} a_2 = -\frac{1}{5} \times (-11) = 2.2$

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Step 3: Find $a_4$

$a_4 = -\frac{1}{5} a_3 = -\frac{1}{5} \times 2.2 = -0.44$

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Step 4: Find $a_5$

$a_5 = -\frac{1}{5} a_4 = -\frac{1}{5} \times (-0.44) = 0.088$

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Final Results:

• $a_2 = -11$
• $a_3 = 2.2$
• $a_4 = -0.44$
• $a_5 = 0.088$

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Would you like further explanation or details on the calculations?

Related Questions:

1. What is the general formula for $a_n$ in this sequence?
2. How do you determine if this sequence converges or diverges?
3. What happens to the terms as $n$ increases indefinitely?
4. How would the sequence change if $a_1$ were different?
5. How can you graph this sequence?

Tip:

When dealing with geometric sequences involving negative ratios, pay attention to the alternating signs in the terms.