Question

Find the next two terms for each sequence. Then write its recursive formula 6, 7, 7.5, 7.75

Answer 1

For each term you're adding half of what you added before. 
So the fifth term is 7.75 + 1/8 = 7.875
the sixth term is 7.875 + 1/16 = 7.9375

a_1 = 6
a_2 = 6 + 1 = 7   =   a_1 + 1 =  a_1 + (½)^0
a_3 = 7 + ½ = 7.5  =   a_2 + ½   = a_2 + (½)^1
a_4 = 7.5 + ¼ = 7.75   =  a_3 + ¼  =  a_3 + (½)^2

So each power of ½ is (n - 2).  The recursive formula is
$a_1=6, a_n=a_{n-1}+(\frac{1}{2})^{n-2}$