find the 59th term of the arithmetic sequence 26, 17, 8, ...

Explanation:

Step1: Find the common difference

The common difference $d$ of an arithmetic sequence is found by subtracting the first - term from the second - term. Here, $a_1 = 26$, $a_2 = 17$, so $d=a_2 - a_1=17 - 26=-9$.

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 $a_n=a_1+(n - 1)d$. We want to find the 59th term, so $n = 59$, $a_1 = 26$, and $d=-9$. Substitute these values into the formula: $a_{59}=26+(59 - 1)\times(-9)$.

Step3: Simplify the expression

First, calculate the value inside the parentheses: $59 - 1 = 58$. Then, multiply: $58\times(-9)=-522$. Finally, add: $a_{59}=26+( - 522)=26-522=-496$.

Answer:

$-496$