How to add numbers from x to y in bash?

Question

bash

Good afternoon. According to the task, it is necessary to add the number from x to y that were entered by the user. And the only thing I thought of was to do the following.

#!/bin/bash
read -p "Type some number: " num
for((i=0;i<${#num};i++)); do ((sum+=${num:i:1})); done

echo "$sum

But there is a problem, all the numbers that will be summed up must be entered.
In this regard, the question is how to make it generate and add numbers?

Answer 1

9th grade, arithmetic progression

# b >= a
read -p "число 1: " a
read -p "число 2: " b
echo $[(a+b)*(b-a+1)/2]