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

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

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

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

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

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

Hence, the first five terms of the sequence are $2,2,1,0$ and $-1$ 

The corresponding series is $2+2+1+0(-1)+\ldots$

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