Answer:
[tex]17860[/tex]
Step-by-step explanation:
To answer this, let's recall a few properties of summations:
[tex]\sum_{i=0}^{n}(a_i+b_i)=\sum_{i=0}^{n}a_i+\sum_{i=0}^{n}b_i\\\\ \sum_{i=0}^{n}(c*a_i)=c*\sum_{i=0}^{n}(a_i)\\\\ \sum_{i=0}^{n}(c)=(n+1)*c[/tex]
With these in mind, we can rewrite the given summation as follows:
[tex]\sum_{n=0}^{75}(6n+10)=\sum_{n=0}^{75}6n+\sum_{n=0}^{75}10=6*\sum_{n=0}^{75}n+76*10\\\\ =6*\frac{75*76}{2} +760=3*75*76+760=17860[/tex]
