write an explicit formula for $a_n$, the $n^{th}$ term of the sequence 19, 13, 7, ....
write an explicit formula for $a_n$, the $n^{th}$ term of the sequence 19, 13, 7, ....
Answer
Explanation:
Step1: Identify the first - term and common difference
The first - term $a_1 = 19$. The common difference $d=13 - 19=-6$.
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 $a_1 = 19$ and $d=-6$ into the formula: $a_n=19+(n - 1)(-6)$.
Step3: Simplify the formula
$a_n=19-6n + 6=25-6n$.
Answer:
$a_n=25 - 6n$