Write an explicit formula for $$ a_{n} $$, the $$ n^{ ext {th }} $$ term of the sequence $$ 39,31,23, \ldots $$ Answer Attempt 1 out of 3 $$ a_{n}=\square $$

Question

Write an explicit formula for $$ a_{n} $$, the $$ n^{	ext {th }} $$ term of the sequence $$ 39,31,23, \ldots $$ 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 $$ 39, 31, 23, \ldots $$, we first need to identify the pattern in the sequence.

1. **Identify the terms:**
   - $$ a_1 = 39 $$
   - $$ a_2 = 31 $$
   - $$ a_3 = 23 $$

2. **Calculate the differences between consecutive terms:**
   - $$ a_2 - a_1 = 31 - 39 = -8 $$
   - $$ a_3 - a_2 = 23 - 31 = -8 $$

The difference between consecutive terms is constant at $$-8$$. This indicates that the sequence is an arithmetic sequence.

3. **General formula for an arithmetic sequence:**
   The general formula for the $$ n^{\text{th}} $$ term of an arithmetic sequence can be expressed as:
   $$
   a_n = a_1 + (n - 1) \cdot d
   $$
   where $$ a_1 $$ is the first term and $$ d $$ is the common difference.

4. **Substituting the known values:**
   - $$ a_1 = 39 $$
   - $$ d = -8 $$

Now we can substitute these values into the formula:
$$
a_n = 39 + (n - 1)(-8)
$$

5. **Simplifying the expression:**
   $$
   a_n = 39 - 8(n - 1)
   $$
   $$
   a_n = 39 - 8n + 8
   $$
   $$
   a_n = 47 - 8n
   $$

Thus, the explicit formula for the $$ n^{\text{th}} $$ term of the sequence is:
$$
a_n = 47 - 8n
$$

So, the final answer is:
$$
a_n = 47 - 8n
$$
The explicit formula for the $$ n^{\text{th}} $$ term of the sequence is $$ a_n = 47 - 8n $$.

Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 39,31,23, \ldots \) Answer Attempt 1 out of 3 \( a_{n}=\square \)

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