Write an explicit formula for $$ a_{n} $$, the $$ n^{ ext {th }} $$ term of the sequence $$ 23,27,31, \ldots $$ 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 $$ 23,27,31, \ldots $$ Answer Attempt 1 out of 3 $$ a_{n}=\square $$

UpStudy AI · Accepted Answer

1. The first term of the sequence is $$ a_1 = 23 $$.

2. The sequence is arithmetic with a common difference computed as:
   $$
   d = 27 - 23 = 4
   $$

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

4. Substitute the known values:
   $$
   a_n = 23 + (n-1) \cdot 4
   $$

5. Simplify the expression:
   $$
   a_n = 23 + 4n - 4 = 4n + 19
   $$

Thus, the explicit formula for the $$ n^{\text{th}} $$ term is:
$$
a_n = 4n + 19
$$
The explicit formula for the $$ n^{\text{th}} $$ term is $$ a_n = 4n + 19 $$.

Write an explicit formula for \( a_{n} \), the \( n^{\text {th }} \) term of the sequence \( 23,27,31, \ldots \) Answer Attempt 1 out of 3 \( a_{n}=\square \)

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