Write the first five terms of the following sequence and obtain the corresponding series:

$a_{1}=a_{2}=2, a_{n}=a_{n-1}-1, n>2$

$\Rightarrow a_{3}=a_{2}-1=2-1=1$

$a_{4}=a_{3}-1=1-1=0$

$a_{5}=a_{4}-1=0-1=-1$

Hence, the first five terms of the sequence are 2, 2, 1, 0, and –1.

The corresponding series is 2 + 2 + 1 + 0 + (–1) + …