If the first term of an arithmetic progression is $a$,the common difference is $1$,and the last term is $b$,what is the sum of the progression?
- A$\frac{(a + b)(1 + a - b)}{2}$
- B$\frac{(a + b)(1 - a + b)}{2}$
- C$\frac{(a + b)(1 - a)}{2}$
- D$(a + b)(1 - a + b)$
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