Chapter 12.1, Problem 67AYU

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

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

To determine

To find: The sum using summation notation: $a+\left(a+d\right)+\left(a+2d\right)+\dots \dots .+\left(a+nd\right)$.

Answer to Problem 67AYU

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

Explanation of Solution

Given:

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

Calculation:

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