Find the sum of first five terms of the G.P. 1,2,4, ….

Answer

To find the sum of the first five terms of the geometric progression (G.P.) given by the sequence 1, 2, 4, ..., we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first term (a) and the common ratio (r)**:
- The first term \( a \) is the first number in the sequence, which is \( 1 \).
- The common ratio \( r \) can be found by dividing the second term by the first term. So, \( r = \frac{T_2}{T_1} = \frac{2}{1} = 2 \).

2. **Determine the number of terms (n)**:
- We need to find the sum of the first five terms, so \( n = 5 \).

3. **Use the formula for the sum of the first n terms of a G.P.**:
- The formula for the sum \( S_n \) of the first \( n \) terms of a G.P. is given by:
\[ S_n = a \frac{r^n - 1}{r - 1} \]
- Here, \( a = 1 \), \( r = 2 \), and \( n = 5 \).

4. **Substitute the values into the formula**:
- Plugging in the values, we get:
\[ S_5 = 1 \cdot \frac{2^5 - 1}{2 - 1} \]

5. **Calculate \( 2^5 \)**:
- \( 2^5 = 32 \).

6. **Subtract 1 from \( 32 \)**:
- \( 32 - 1 = 31 \).

7. **Divide by \( 2 - 1 \)**:
- \( 31 \div 1 = 31 \).

8. **Final result**:
- Therefore, the sum of the first five terms of the G.P. is \( S_5 = 31 \).

### Summary:
The sum of the first five terms of the G.P. 1, 2, 4, ... is **31**.