Find the G.P. whose first term is 64 and next term is 32.

Answer

To find the geometric progression (G.P.) whose first term is 64 and the second term is 32, we can follow these steps:

### Step 1: Identify the first and second terms
Let the first term \( t_1 = 64 \) and the second term \( t_2 = 32 \).

### Step 2: Find the common ratio
The common ratio \( r \) of a G.P. can be found using the formula:
\[ r = \frac{t_2}{t_1} \]
Substituting the values:
\[ r = \frac{32}{64} = \frac{1}{2} \]

### Step 3: Calculate the subsequent terms
Now that we have the common ratio, we can find the next terms in the G.P.

- **Third term \( t_3 \)**:
\[ t_3 = r \times t_2 = \frac{1}{2} \times 32 = 16 \]

- **Fourth term \( t_4 \)**:
\[ t_4 = r \times t_3 = \frac{1}{2} \times 16 = 8 \]

- **Fifth term \( t_5 \)**:
\[ t_5 = r \times t_4 = \frac{1}{2} \times 8 = 4 \]

### Step 4: Write the G.P.
Now we can write the G.P. using the terms we have calculated:
\[ \text{G.P.} = 64, 32, 16, 8, 4, \ldots \]

### Final Answer:
The required geometric progression is:
\[ 64, 32, 16, 8, 4, \ldots \]

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