Find the 6th term of 2,4,8,……….

Answer

To find the 6th term of the sequence 2, 4, 8, ..., we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first term (a)**:
The first term of the sequence is given as:
\[ a = 2 \]

2. **Determine the common ratio (r)**:
To find the common ratio, we can divide the second term by the first term:
\[ r = \frac{t_2}{t_1} = \frac{4}{2} = 2 \]
We can verify this by checking the ratio of the third term to the second term:
\[ r = \frac{t_3}{t_2} = \frac{8}{4} = 2 \]
Thus, the common ratio \( r \) is confirmed to be 2.

3. **Use the formula for the nth term of a geometric sequence**:
The nth term of a geometric sequence can be calculated using the formula:
\[ t_n = a \cdot r^{n-1} \]
For the 6th term (\( n = 6 \)):
\[ t_6 = a \cdot r^{6-1} = 2 \cdot 2^{5} \]

4. **Calculate \( 2^5 \)**:
We calculate \( 2^5 \):
\[ 2^5 = 32 \]

5. **Multiply by the first term (a)**:
Now we multiply this result by the first term:
\[ t_6 = 2 \cdot 32 = 64 \]

### Final Answer:
The 6th term of the sequence is:
\[ \boxed{64} \]

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