find the 73rd term of the arithmetic sequence -28, -41, -54, ...

Explanation:

Step1: Identify first - term and common - difference

The first term $a_1=-28$, and the common difference $d=-41 - (-28)=- 13$.

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 $n = 73$, $a_1=-28$, and $d=-13$ into the formula: $a_{73}=-28+(73 - 1)\times(-13)$.

Step3: Calculate the value

First, calculate $73−1 = 72$. Then, $72\times(-13)=-936$. Finally, $a_{73}=-28-936=-964$.

Answer:

$-964$