Question

Please help with #5 only

Answer 1

1680

Explanation:

`\sum\limits_(n=1)^(42)2n-3\\\\a_n=2n-3\\\\a_(n+1)=2(n+1)-3=2n+2-3=2n-1\\\\a_(n+1)-a_n=(2n-1)-(2n-3)=2n-1-2n+3=2=constant\\\\\text{Therefore it's an arithmetic sequence with first term}\\\\a_1=2(1)-3=2-3=-1\\\\\text{and common difference}\\\\d=2`

`\text{The formula of a sum of terms of an aithmetic sequence:}\\\\S_n=(2a_1+(n-1)d)/(2)\cdot n\\\\\text{Substitute:}\\\\n=42,\ a_1=-1,\ d=2:\\\\S_(42)=(2(-1)+(42-1)(2))/(2)\cdot42=[-2+(41)(2)](21)=(-2+82)(21)\\\\=(80)(21)=1680`