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
[tex]a_1=6, a_n=a_{n-1}+(\frac{1}{2})^{n-2}[/tex]
