Find the sum of the product of the corresponding terms of the sequences 2,4,8,16,32 and 128,32,8,2,`(1)/(2)`.

Explanation

To find the sum of the product of the corresponding terms of the sequences \(2, 4, 8, 16, 32\) and \(128, 32, 8, 2, \frac{1}{2}\), we will follow these steps:

### Step 1: Identify the corresponding terms
The two sequences are:
- First sequence: \(2, 4, 8, 16, 32\)
- Second sequence: \(128, 32, 8, 2, \frac{1}{2}\)

We will pair the corresponding terms:
- First term: \(2\) and \(128\)
- Second term: \(4\) and \(32\)
- Third term: \(8\) and \(8\)
- Fourth term: \(16\) and \(2\)
- Fifth term: \(32\) and \(\frac{1}{2}\)

### Step 2: Calculate the products of the corresponding terms
Now we will calculate the product of each pair:
1. \(2 \times 128 = 256\)
2. \(4 \times 32 = 128\)
3. \(8 \times 8 = 64\)
4. \(16 \times 2 = 32\)
5. \(32 \times \frac{1}{2} = 16\)

### Step 3: Sum the products
Now, we will sum all the products calculated in the previous step:
\[ 256 + 128 + 64 + 32 + 16 \]

### Step 4: Perform the addition
Calculating the sum step-by-step:
1. \(256 + 128 = 384\)
2. \(384 + 64 = 448\)
3. \(448 + 32 = 480\)
4. \(480 + 16 = 496\)

Thus, the final sum of the products is:
\[ \text{Sum} = 496 \]

### Final Answer
The sum of the product of the corresponding terms of the sequences is \(496\).

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