Question

In Problems 61–70, express each sum using summation notation.

$a+\left(a+d\right)+\left(a+2d\right)+........+\left(a+nd\right)$

Short answer

The required summation notation is $a+\left(a+d\right)+\left(a+2d\right)+........+\left(a+nd\right)=\sum _{k=0}^n\left(a+kd\right)$

Step-by-step solution

Step 1. Write the given information.

The given sum is:

$a+\left(a+d\right)+\left(a+2d\right)+........+\left(a+nd\right)$

Step 2. Write the sum using summation notation.

As we can see that the sum $a+\left(a+d\right)+\left(a+2d\right)+........+\left(a+nd\right)$has $n+1$terms, starts at $k=0$and ends at $k=n$.

Therefore, $a+\left(a+d\right)+\left(a+2d\right)+........+\left(a+nd\right)=\sum _{k=0}^n\left(a+kd\right)$.