Determine whether the given sequence is arithmetic, geometric, or neither.

Step 1
Since the expression is a linear function of "n". So it is arithmetic sequence.
Common difference is the coefficient of "n" that is $=-\frac{10}{11}$
Step 2
We will use the sum formula of first n natural numbers.
$\sum _{n=1}^{50}(9-\frac{10}{11}n)=\sum _{n=1}^{50}(9-\frac{10}{11n})\sum _{n=1}^{50}n$
$=9(50)-\frac{10}{11}\times \frac{50(50+1)}{2}$
$=450-\frac{10}{11}\times \frac{50(51)}{2}$
$=450-\frac{12750}{11}$
$=-\frac{7800}{11}$
Answer: Aritmetic sequence common difference $=-\frac{10}{11}$
$\sum =-\frac{7800}{11}$