Question

Recursive formula of 6, 7, 7.5, 7.75

Answer 1

The answer is: 6, 7, 7 1/2, 7 3/4.

Answer 2

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