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

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:** \[ T_{5} = \frac{1}{8} \]