representing a sequence with an explicit function\nthe first five terms of an arithmetic sequence are shown…

representing a sequence with an explicit function\nthe first five terms of an arithmetic sequence are shown below:\n20, 17, 14, 11, 8, ...\nlet n represent the term number and f(n) the term in the sequence.\nthe function represents the sequence.

representing a sequence with an explicit function\nthe first five terms of an arithmetic sequence are shown below:\n20, 17, 14, 11, 8, ...\nlet n represent the term number and f(n) the term in the sequence.\nthe function represents the sequence.

Answer

Answer:

$f(n)=23 - 3n$

Explanation:

Step1: Identify the first - term and common difference

The first term $a_1 = 20$. The common difference $d=17 - 20=- 3$.

Step2: Use the formula for the $n$th term of an arithmetic sequence

The formula for the $n$th term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. Substitute $a_1 = 20$ and $d=-3$ into the formula: $a_n=20+(n - 1)(-3)$.

Step3: Simplify the formula

Expand the expression: $a_n=20-3n + 3$. Combine like - terms: $a_n=23 - 3n$. So $f(n)=23 - 3n$.