Recursive formula of 6, 7, 7.5, 7.75

6, 7, 7.5, 7.75

If we look, after the first two number, the next is gotten by adding half of the difference of the two numbers before to the last number.

6, 7

The next is:

7 - 6 = 1, 

1/2 = 0.5

7 + 0.5 = 7.5  So the next is 7.5.

So we have  7 and 7.5

7.5 - 7 = 0.5

0.5/2 = 0.25

7.5 + 0.25 = 7.75

So if we have  Tₓ,  Tₓ₊₁,

So by observation, we can say the recursive formula is:

Tₓ₊₂  =   Tₓ₊₁ + (Tₓ₊₁ - Tₓ)/2