Instead of numbering the fruits starting with 1, let's number them
starting with 0, that is:

0 = banana
1 = coconut
2 = grape
3 = melon
4 = kiwi
5 = berry
6 = banana
7 = coconut
8 = grape
9 = melon
10 = kiwi
11 = berry
12 = banana
...

That way each multiple of 6 is banana. So to find
the nth fruit, we only need to divide n by 6 and take
the remainder.  If the remainder is 0, the fruit is
banana. If the remainder is 1 then the fruit is coconut,
and so forth up to a remainder of 5 which will give the
fruit berry.

Since we started numbering with 0 instead of 1, the
75103rd fruit will actually be the 75102nd fruit by
our system of numbering.

[That's because since fruit #1 is what we are calling 
fruit #0, then fruit #75103 would be what we would be 
calling fruit #75102.]

So we divide 75102 by 6

         12517 
       6)75102  
         6
         15
         12
          31
          30
           10
            6
            42
            42
             0

The remainder is 0, so the answer is 'banana'.

Edwin