Write the explicit formula that represents the sequence below. Then find A(12). $$ 189,199,209,219, \ldots $$

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To find the explicit formula for the sequence $$ 189, 199, 209, 219, \ldots $$, we first need to identify the pattern in the sequence.

1. **Identify the first term and the common difference:**
   - The first term $$ A(1) = 189 $$.
   - The common difference $$ d $$ can be calculated as follows:
     $$
     d = 199 - 189 = 10
     $$

2. **General formula for an arithmetic sequence:**
   The explicit formula for the $$ n $$-th term of an arithmetic sequence is given by:
   $$
   A(n) = A(1) + (n - 1) \cdot d
   $$
   Substituting the known values:
   $$
   A(n) = 189 + (n - 1) \cdot 10
   $$

3. **Simplifying the formula:**
   $$
   A(n) = 189 + 10n - 10 = 10n + 179
   $$

Thus, the explicit formula for the sequence is:
$$
A(n) = 10n + 179
$$

4. **Finding $$ A(12) $$:**
   Now, we can find $$ A(12) $$ by substituting $$ n = 12 $$ into the formula:
   $$
   A(12) = 10 \cdot 12 + 179
   $$

Let's calculate $$ A(12) $$:
$$
A(12) = 120 + 179 = 299
$$

Therefore, the value of $$ A(12) $$ is $$ 299 $$.
The explicit formula for the sequence is $$ A(n) = 10n + 179 $$. When $$ n = 12 $$, $$ A(12) = 299 $$.

Write the explicit formula that represents the sequence below. Then find A(12). \( 189,199,209,219, \ldots \)

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