Answer:
Option C is correct.
[tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]
Step-by-step explanation:
Given the expression: [tex]\sum_{i=1}^{18} (7i^2+9)[/tex]
Using properties of summation:
- [tex]\sum_{i=1}^{n} (a+bi) =\sum_{i=1}^{n} a + \sum_{i=1}^{n} bi[/tex]
- [tex]\sum_{i=1}^{n} a = an[/tex]
Using properties of summation in the given expression we have;
[tex]\sum_{i=1}^{18} (7i^2+9)[/tex]
= [tex]\sum_{i=1}^{18} 7i^2 + \sum_{i=1}^{18} 9[/tex]
=[tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]
Therefore, the following given expression uses the properties of summation to represents is, [tex]7 \cdot \sum_{i=1}^{18} i^2 + 9 \cdot 18[/tex]
