Answer:
36
Step-by-step explanation:
We have the summation:
[tex]\displaystyle{\sum_{i=1}^{9} 2i-6[/tex]
Essentially, we want to find the sum of (2i-6) from i=1 to i=9.
First, using summation properties, we can split this to:
[tex]=\displaystyle{\sum_{i=1}^{9} 2i+\displaystyle{\sum_{i=1}^{9} -6[/tex]
On the right, it will simply be -6 evaluated 9 times. We can also move the constant out from the left:
[tex]=\displaystyle{2\sum_{i=1}^{9} i+9(-6)[/tex]
For the summation on the left, this will simply be the sum (1+2+3+...+9). This yields 45. Therefore:
[tex]=2(45)+9(-6)[/tex]
Evaluate:
[tex]=90-54=36[/tex]
So, our final answer is 36.
