# Evaluate sum from n=3 to 12 of -5n-1

Split the summation to make the starting value of equal to .
Evaluate .
Split the summation into smaller summations that fit the summation rules.
Evaluate .
The formula for the summation of a polynomial with degree is:
Substitute the values into the formula and make sure to multiply by the front term.
Simplify.
Multiply by .
Divide by .
Multiply by .
Evaluate .
The formula for the summation of a constant is:
Substitute the values into the formula.
Simplify.
Remove parentheses.
Multiply by .
Add the results of the summations.
Subtract from .
Evaluate .
Expand the series for each value of .
Simplify.
Simplify each term.
Multiply by .
Multiply by .
Simplify by subtracting numbers.
Subtract from .
Subtract from .
Subtract from .
Replace the summations with the values found.