Find the Sum of the Series 7.6+6.3+5+3.7+2.4+1.1+(-0.2)+(-1.5)

This is the formula to find the sum of the first ${\displaystyle n}$ terms of the sequence. To evaluate it, the values of the first and ${\displaystyle n}$th terms must be found.

This is an arithmetic sequence since there is a common difference between each term. In this case, adding ${\displaystyle -1.3}$ to the previous term in the sequence gives the next term. In other words, ${\displaystyle a_n=a_1+d(n-1)}$.

This is the formula of an arithmetic sequence.

Substitute in the values of ${\displaystyle a_1=7.6}$ and ${\displaystyle d=-1.3}$.

Add ${\displaystyle 7.6}$ and ${\displaystyle 1.3}$.

Substitute in the value of ${\displaystyle n}$ to find the ${\displaystyle n}$th term.

Multiply ${\displaystyle -1.3}$ by ${\displaystyle 8}$.

Add ${\displaystyle -10.4}$ and ${\displaystyle 8.9}$.

Replace the variables with the known values to find ${\displaystyle S_8}$.

Divide ${\displaystyle 8}$ by ${\displaystyle 2}$.

Subtract ${\displaystyle 1.5}$ from ${\displaystyle 7.6}$.

Multiply ${\displaystyle 4}$ by ${\displaystyle 6.1}$.