Question

3/20 , 3/10 , 9/20 , 3/5 ...

Find terms of an arithmetic sequence.
What's the next fraction in this sequence? Simply your answer.

Answer 1

3/20, 6/20, 9/20, 12/20 so the common difference is 3/20, ie each term is 3/20 greater than the term preceding it. Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number, in this case:

a(n)=3/20+(3/20)(n-1)

a(n)=3/20+3n/20-3/20

a(n)=3n/20 so the 5th term is:

a(4)=3*5/20=15/20=3/4