Write an explicit formula for $$ a_{n} $$, the $$ n^{ ext {th }} $$ term of the sequence $$ 31,27,23, \ldots $$. Answer Altemptiout of 3 $$ a_{n}=\square $$ Submit Answer

Question

Write an explicit formula for $$ a_{n} $$, the $$ n^{	ext {th }} $$ term of the sequence $$ 31,27,23, \ldots $$. Answer Altemptiout of 3 $$ a_{n}=\square $$ Submit Answer

UpStudy AI · Accepted Answer

To find the explicit formula for the $$ n^{\text{th}} $$ term of the sequence $$ 31, 27, 23, \ldots $$, we first need to identify the pattern in the sequence.

1. **Identify the first term and the common difference:**
   - The first term $$ a_1 = 31 $$.
   - The second term $$ a_2 = 27 $$.
   - The third term $$ a_3 = 23 $$.

2. **Calculate the common difference:**
   - The difference between the first and second term: $$ 27 - 31 = -4 $$.
   - The difference between the second and third term: $$ 23 - 27 = -4 $$.

Thus, the common difference $$ d = -4 $$.

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:
   $$
   a_n = a_1 + (n - 1) \cdot d
   $$
   Substituting the known values:
   - $$ a_1 = 31 $$
   - $$ d = -4 $$

We get:
   $$
   a_n = 31 + (n - 1)(-4)
   $$

4. **Simplify the expression:**
   $$
   a_n = 31 - 4(n - 1)
   $$
   $$
   a_n = 31 - 4n + 4
   $$
   $$
   a_n = 35 - 4n
   $$

Thus, the explicit formula for the $$ n^{\text{th}} $$ term of the sequence is:
$$
a_n = 35 - 4n
$$

So, the final answer is:
$$
\boxed{35 - 4n}
$$
The explicit formula for the $$ n^{\text{th}} $$ term is $$ a_n = 35 - 4n $$.

Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 31,27,23, \ldots \). Answer Altemptiout of 3 \( a_{n}=\square \) Submit Answer

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