Write an explicit formula for $$ a_{n} $$, the $$ n^{ ext {th }} $$ term of the sequence $$ 25,33,41, \ldots $$ Answer Attempt 1 out of 3 $$ a_{n}=\square $$

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Write an explicit formula for $$ a_{n} $$, the $$ n^{	ext {th }} $$ term of the sequence $$ 25,33,41, \ldots $$ Answer Attempt 1 out of 3 $$ a_{n}=\square $$

UpStudy AI · Accepted Answer

To find the explicit formula for the $$ n^{\text{th}} $$ term of the sequence $$ 25, 33, 41, \ldots $$, we first need to identify the pattern in the sequence.

1. **Identify the first term and the common difference:**
   - The first term $$ a_1 = 25 $$.
   - The second term $$ a_2 = 33 $$.
   - The third term $$ a_3 = 41 $$.

2. **Calculate the common difference:**
   - $$ a_2 - a_1 = 33 - 25 = 8 $$
   - $$ a_3 - a_2 = 41 - 33 = 8 $$

The common difference $$ d = 8 $$.

3. **Use the formula for the $$ n^{\text{th}} $$ term of an arithmetic sequence:**
   The formula for the $$ n^{\text{th}} $$ term of an arithmetic sequence is given by:
   $$
   a_n = a_1 + (n - 1) \cdot d
   $$

4. **Substituting the known values:**
   - $$ a_1 = 25 $$
   - $$ d = 8 $$

Therefore, the formula becomes:
   $$
   a_n = 25 + (n - 1) \cdot 8
   $$

5. **Simplifying the formula:**
   $$
   a_n = 25 + 8n - 8 = 8n + 17
   $$

Thus, the explicit formula for the $$ n^{\text{th}} $$ term of the sequence is:
$$
a_n = 8n + 17
$$

So, the answer is:
$$
a_{n} = 8n + 17
$$
The explicit formula for the $$ n^{\text{th}} $$ term of the sequence is $$ a_{n} = 8n + 17 $$.

Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 25,33,41, \ldots \) Answer Attempt 1 out of 3 \( a_{n}=\square \)

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