Question

find the 75th term of the arithmetic sequence -17, -13, -9, ... type your answer in the boxes

Explanation:

Step1: Identify sequence parameters

First term $a_1 = -17$, common difference $d = -13 - (-17) = 4$, target term $n=75$.

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:
$a_{75} = -17 + (75-1) \times 4$

Step3: Simplify the expression

First calculate $(75-1)=74$, then $74 \times 4 = 296$.
$a_{75} = -17 + 296$

Step4: Compute final value

$a_{75} = 279$

Answer:

279