A sequence starts $$ -3,1,5,9 \ldots $$ a. Write the equation in "first term"

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To find the equation of the sequence given by the terms $$ -3, 1, 5, 9, \ldots $$, we first need to identify the pattern in the sequence.

1. **Identify the first term**: The first term $$ a_1 $$ is $$ -3 $$.

2. **Identify the common difference**: We can find the common difference $$ d $$ by subtracting consecutive terms:
   - $$ 1 - (-3) = 4 $$
   - $$ 5 - 1 = 4 $$
   - $$ 9 - 5 = 4 $$

The common difference $$ d $$ is $$ 4 $$.

3. **Write the general term**: The general term of an arithmetic sequence can be expressed as:
   $$
   a_n = a_1 + (n - 1) \cdot d
   $$
   where $$ a_n $$ is the $$ n $$-th term, $$ a_1 $$ is the first term, $$ d $$ is the common difference, and $$ n $$ is the term number.

4. **Substituting the known values**:
   - $$ a_1 = -3 $$
   - $$ d = 4 $$

Thus, the equation becomes:
   $$
   a_n = -3 + (n - 1) \cdot 4
   $$

Now, let's simplify this equation:
$$
a_n = -3 + 4n - 4 = 4n - 7
$$

Therefore, the equation for the $$ n $$-th term of the sequence is:
$$
a_n = 4n - 7
$$
The equation for the $$ n $$-th term of the sequence is $$ a_n = 4n - 7 $$.

A sequence starts \( -3,1,5,9 \ldots \) a. Write the equation in "first term"

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