Find the 15th term of the G.P -2,2,-2,….

Options

A. -22
B. 2
C. -2
D. none of these

Answer

To find the 15th term of the geometric progression (G.P.) given by the sequence -2, 2, -2, ..., we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first term (a)**:
The first term of the G.P. is:
\[ a = -2 \]

2. **Determine the common ratio (r)**:
The common ratio can be found by dividing the second term by the first term:
\[ r = \frac{T_2}{T_1} = \frac{2}{-2} = -1 \]

3. **Use the formula for the nth term of a G.P.**:
The formula for the nth term of a G.P. is given by:
\[ T_n = a \cdot r^{n-1} \]
We need to find the 15th term, so we substitute \( n = 15 \):
\[ T_{15} = a \cdot r^{15-1} = a \cdot r^{14} \]

4. **Substitute the values of a and r**:
Now substitute \( a = -2 \) and \( r = -1 \):
\[ T_{15} = -2 \cdot (-1)^{14} \]

5. **Calculate \((-1)^{14}\)**:
Since 14 is an even number, \((-1)^{14} = 1\):
\[ T_{15} = -2 \cdot 1 \]

6. **Final calculation**:
Therefore, the 15th term is:
\[ T_{15} = -2 \]

### Conclusion:
The 15th term of the G.P. is \(-2\).

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