Question

the first five terms of a sequence are a1 = 47, a2 = 33, a3 = 19, a4 = 5, and a5 = - 9. based on this information, create an equation that can be used to find the nth term of the sequence, an. move the correct answer to each box. each answer may be used more than once. not all answers will be used.

Explanation:

Step1: Find the common - difference

The common - difference $d$ of an arithmetic sequence is given by $d=a_{n + 1}-a_{n}$. Let's take $a_1 = 47$, $a_2 = 33$. Then $d=a_2 - a_1=33 - 47=-14$.

Step2: Recall the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is $a_{n}=a_1+(n - 1)d$, where $a_1$ is the first - term and $d$ is the common difference.

Step3: Substitute the values of $a_1$ and $d$ into the formula

Since $a_1 = 47$ and $d=-14$, the formula for the nth term of the sequence is $a_{n}=47+(n - 1)(-14)$.

Step4: Simplify the formula

Expand the expression: $a_{n}=47-14n + 14=61-14n$.

Answer:

$a_{n}=61 - 14n$