Question

a roofs is constructed with a pole 10 m high. A spider jumps 2 m and then slips 1 m. In how many times will the spider reach the roof.

Answer 1

9 jumps 
1jump=(2-1)m
but on the last jump he will be on the top 

Answer 2

height of the pole : 10 m.  jump amount each attempt:  2 m. 
slipping amount each time:  1 m.

the jump      height      slipped        final
number       reached    height        position
                                                   0m
 1                 2m         1m            1 m
2                  3m          1m            2m
       :
       :
8                 9m            1m            8m
9                 10m 

Thus after the 9th attempt/jump, the spider reaches the top of the pole/roof.  Since it goes to the horizontal position, spider does not slip down.
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from the first two attempts/jumps, we see that the spider's final position N meters is equal to the number of jumps N.

we need to find when the spider attains 10 m (target height) - 2 m (jumping height) = 8 meters.  Because, from 8 m  the spider can reach the top and stay there without slipping.

So to attain 8 m (after slipping), it takes 8 attempts.  In the 9th attempt, the spider goes to the top.