Question 100069
1/2,3,11/2,8,21/2...

Since most of the terms are in "halves". Good way how to start this problem is by coverting the integers in it into halves.It's generally good to have 1 type of numbers in pronlem either integers or fractions etc...

So 3 = 3*2/2 and 8= 8*2/2 , thus 3 = 6/2 and 8 = 16/2 and we get 1/2 , 6/2 , 11/2 , 16/2 , 21/2 ...Easy to see that every numerator is increased by 5.

It is arithmetic sequence. Formula for n-th term of arithmetic sequence is {{{A[n]= A1+(n-1)*d}}} where d is increment you want to add each time.

We can write : {{{A[n]=1/2+5/2*(n-1)}}} or {{{A[n] = (1+5*(n-1))/2}}}

Concerning your second problem I am quite sure you'll be able to finish it yourself. Good luck!