Find the 7th term of the G.P. 4 ,-8 , 16, ... .

Explanation

To find the 7th term of the geometric progression (G.P.) given by the sequence 4, -8, 16, ..., we can follow these steps:

### Step 1: Identify the first term (A) and common ratio (R)
The first term of the G.P. is:
\[ A = 4 \]

To find the common ratio (R), we can divide the second term by the first term:
\[ R = \frac{\text{Second term}}{\text{First term}} = \frac{-8}{4} = -2 \]

### Step 2: Use the formula for the nth term of a G.P.
The formula for the nth term of a G.P. is given by:
\[ A_n = A \cdot R^{n-1} \]

### Step 3: Substitute values to find the 7th term (A7)
To find the 7th term, we substitute \( n = 7 \):
\[ A_7 = A \cdot R^{7-1} = A \cdot R^6 \]

Substituting the values of A and R:
\[ A_7 = 4 \cdot (-2)^{6} \]

### Step 4: Calculate \( (-2)^6 \)
Calculating \( (-2)^6 \):
\[ (-2)^6 = 64 \]

### Step 5: Multiply to find A7
Now substitute back to find \( A_7 \):
\[ A_7 = 4 \cdot 64 = 256 \]

### Final Answer
Thus, the 7th term of the G.P. is:
\[ A_7 = 256 \]

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