Find which of the following is a G.P. :
4,8,16 , . . . . . . . . . . . . .

Answer

To determine if the sequence 4, 8, 16, ... is a geometric progression (G.P.), we will follow these steps:

### Step 1: Identify the terms of the sequence
Let’s denote the terms of the sequence:
- First term (T1) = 4
- Second term (T2) = 8
- Third term (T3) = 16

### Step 2: Use the G.P. condition
For a sequence to be a G.P., the ratio of consecutive terms must be constant. This means that:
\[ \frac{T2}{T1} = \frac{T3}{T2} \]

### Step 3: Calculate the ratios
Now, we will calculate the ratios:
- Calculate \(\frac{T2}{T1}\):
\[ \frac{T2}{T1} = \frac{8}{4} = 2 \]

- Calculate \(\frac{T3}{T2}\):
\[ \frac{T3}{T2} = \frac{16}{8} = 2 \]

### Step 4: Compare the ratios
Now we compare the two ratios:
\[ \frac{T2}{T1} = 2 \quad \text{and} \quad \frac{T3}{T2} = 2 \]

Since both ratios are equal, we can conclude that the sequence is a G.P.

### Conclusion
The sequence 4, 8, 16, ... is a geometric progression with a common ratio of 2.

---