$$ 32 ; 8 ; 2 ; 0,5 ; \ldots $$ Calculate the value of the fifth term, $$ T_{5} $$, of this sequence. INSTRUCTION: Your answer should be exact - do not round off. Answer: $$ T_{5}=\square $$

Question

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The given sequence is:

$$ 32 ; 8 ; 2 ; 0.5 ; \ldots $$

To find the fifth term $$ T_{5} $$, we first identify the pattern of the sequence.

**Step 1: Determine the Common Ratio**

Let's examine how the sequence progresses:

$$
\frac{8}{32} = \frac{1}{4}, \quad \frac{2}{8} = \frac{1}{4}, \quad \frac{0.5}{2} = \frac{1}{4}
$$

The common ratio $$ r $$ is $$ \frac{1}{4} $$.

**Step 2: Use the Geometric Sequence Formula**

The formula for the $$ n $$-th term of a geometric sequence is:

$$
T_{n} = T_{1} \times r^{(n-1)}
$$

Where:
- $$ T_{1} = 32 $$
- $$ r = \frac{1}{4} $$
- $$ n = 5 $$

**Step 3: Calculate $$ T_{5} $$**

$$
T_{5} = 32 \times \left(\frac{1}{4}\right)^{4} = 32 \times \frac{1}{256} = \frac{32}{256} = \frac{1}{8}
$$

**Answer:**
$$
T_{5} = \frac{1}{8}
$$
$$ T_{5} = \frac{1}{8} $$

Calculate the value of the fifth term, , of
this sequence.
INSTRUCTION: Your answer should be
exact - do not round off.
Answer:

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