Question

write explicit formula for sequence question write an explicit formula for $a_n$, the $n^{\text{th}}$ term of the sequence $25, 33, 41, \dots$. answer attempt 1 out of 2 $a_n = $

Explanation:

Step1: Identify sequence type (arithmetic)

This is an arithmetic sequence, where the common difference $d$ is found by subtracting consecutive terms: $d = 33 - 25 = 8$.

Step2: Recall arithmetic sequence formula

The explicit formula for an arithmetic sequence is $a_n = a_1 + (n-1)d$, where $a_1$ is the first term.

Step3: Substitute known values

Here, $a_1 = 25$ and $d = 8$. Substitute these into the formula:
$a_n = 25 + (n-1) \times 8$

Step4: Simplify the expression

Expand and combine like terms:
$a_n = 25 + 8n - 8 = 8n + 17$

Answer:

$a_n = 8n + 17$