Respuesta :
Step-by-step explanation:
Let's start with the first part: The equation for GoP₂ is as follows:
GoP2 A = a^2 - 5at + t^2
GoP² B = b^2 - 5bt + t^2
Where a and b are the coefficients for t^2 and t of A and B, respectively. We know that the 4th and 3rd terms of GoP₂ A and B are 36 and 54, respectively. Therefore, we can substitute these values into the GoP₂ equations for A and B:
36 = a^2 - 5at + t^2
54 = b^2 - 5bt + t^2
Substituting the second equation into the first equation, we get:
36 = (b^2 - 5bt + t^2) - (5at) + t^2
Simplifying, we get:
36 = b^2 - 5bt
Dividing both sides by -b, we get:
t = 6/b
Substituting this value of t into either of the GoP₂ equations, we can solve for a:
a^2 - 5at + t^2 = 36
a^2 - (5*6/b)*a + (6/b)^2 = 36
Simplifying, we get:
a = -b + 6/b
a = (6 - b)/b
Now, let's move on to the second part: The sum of the first four terms of A and B if r = 2. If r = 2, then the first four terms of A are as follows:
a + ar + ar^2 + ar^3 = a + ar(1 + r + r^2 + r^3)
Simplifying, we get:
a + ar(5)
Therefore, the sum of the first four terms of A is 5a. Similarly, the sum of the first four terms of B is 5b. So the sum of the first four terms of A and B is 5a + 5b.
