Check whether the given sequences form a G.P. or not :
8 , 24 , 72 , 216, . . . . . . . . .

Answer

To determine whether the given sequence \(8, 24, 72, 216, \ldots\) forms a geometric progression (G.P.), we need to check if the ratio between consecutive terms is constant.

### Step-by-Step Solution:

1. **Identify the Terms**:
The given sequence is \( t_1 = 8 \), \( t_2 = 24 \), \( t_3 = 72 \), \( t_4 = 216 \).

2. **Calculate the Common Ratio**:
The common ratio \( r \) of a G.P. is calculated using the formula:
\[ r = \frac{t_n}{t_{n-1}} \]
where \( t_n \) is the nth term and \( t_{n-1} \) is the previous term.

3. **Calculate \( r \) for the First Pair**:
For the first two terms:
\[ r = \frac{t_2}{t_1} = \frac{24}{8} = 3 \]

4. **Calculate \( r \) for the Second Pair**:
For the second and third terms:
\[ r = \frac{t_3}{t_2} = \frac{72}{24} = 3 \]

5. **Calculate \( r \) for the Third Pair**:
For the third and fourth terms:
\[ r = \frac{t_4}{t_3} = \frac{216}{72} = 3 \]

6. **Conclusion**:
Since the common ratio \( r \) is the same for all pairs of consecutive terms (i.e., \( r = 3 \)), we can conclude that the sequence forms a geometric progression.

### Final Answer:
Hence, the sequence \( 8, 24, 72, 216, \ldots \) forms a G.P.