Respuesta :

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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
facundo3141592

A recursive formula is a formula that gives information of the n-th term using the previous term or terms in a sequence.

Here, we have the sequence:

6, 7, 7.5, 7.75

Let's study the difference between the known terms of the sequence.

The difference between the first two is:

7 - 6 = 1

the difference between the third and second terms is:

7.5 - 7 = 0.5  (half than before)

The difference between the fourth and third terms is:

7.75 - 7.5 = 0.25 (half than before)

So we can see that the difference reduces by half each time.

So defining:

A₀ = 6

A₁ = 7

A₂ = 7.5

A₃ = 7.75

We can see that:

A₁ = A₀ + 1

A₂ = A₁ + 0.5 = A₁ + 1/2

A₃ = A₂ + 0.25 = A₂ + (1/2)^2

Then we can make the general rule for the n-th term as:

Aₙ = Aₙ₋₁ + (1/2)^(n - 1)

Then the recursive formula is just:

Aₙ = Aₙ₋₁ + (1/2)^(n - 1)

with

A₀ = 6

If you want to learn more, you can read:

https://brainly.com/question/11679190

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