Question

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

Explanation:

Step1: Identify sequence parameters

First term $a_1 = 26$, common difference $d = 17 - 26 = -9$, target term $n = 59$.

Step2: Use arithmetic sequence formula

The formula for the $n$-th term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$.
Substitute values:
$a_{59} = 26 + (59 - 1)(-9)$

Step3: Simplify the expression

Calculate $(59 - 1) = 58$, then $58 \times (-9) = -522$.
$a_{59} = 26 - 522$

Step4: Compute final value

$a_{59} = -496$

Answer:

-496