Find the first four terms and the eleventh term of the series whose nth term is 4n-2

Answer

To find the first four terms and the eleventh term of the series whose nth term is given by the formula \( a_n = 4n - 2 \), we will follow these steps:

### Step 1: Find the first term (n=1)
We substitute \( n = 1 \) into the formula:
\[ a_1 = 4(1) - 2 = 4 - 2 = 2 \]

### Step 2: Find the second term (n=2)
Next, we substitute \( n = 2 \):
\[ a_2 = 4(2) - 2 = 8 - 2 = 6 \]

### Step 3: Find the third term (n=3)
Now, we substitute \( n = 3 \):
\[ a_3 = 4(3) - 2 = 12 - 2 = 10 \]

### Step 4: Find the fourth term (n=4)
Next, we substitute \( n = 4 \):
\[ a_4 = 4(4) - 2 = 16 - 2 = 14 \]

### Step 5: Find the eleventh term (n=11)
Finally, we substitute \( n = 11 \):
\[ a_{11} = 4(11) - 2 = 44 - 2 = 42 \]

### Summary of Results
The first four terms of the series are:
- \( a_1 = 2 \)
- \( a_2 = 6 \)
- \( a_3 = 10 \)
- \( a_4 = 14 \)

The eleventh term is:
- \( a_{11} = 42 \)