find the 65th term of the arithmetic sequence -10, 9, 28, ...

Explanation:

Step1: Identify the first - term and common difference

The first - term $a_1=-10$, and the common difference $d = 9-(-10)=19$.

Step2: Use the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. Here, $n = 65$, $a_1=-10$, and $d = 19$. Substitute these values into the formula: $a_{65}=-10+(65 - 1)\times19$.

Step3: Calculate the value

First, calculate $65−1 = 64$. Then, $64\times19=1216$. Finally, $a_{65}=-10 + 1216=1206$.

Answer:

$1206$