The following gives a geometic sequence 2, P Q 250 find the values of P and Q

THE FOLLOWING GIVE A GEOMETRIC SEQUENCE: 2, p, q 250 FIND THE VALUE OF P AND Q

Thank you very much

We know that given a ratio of r,

P = 2r
Q = 2r²
250 = 2r³, so r=5

P=10
Q=50

Do the right solving

To find the values of P and Q in the geometric sequence 2, P, Q, 250, we can use the formula for a geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a constant ratio.

Let's identify the ratio between the terms. We divide any term by its previous term to get the common ratio:

P/2 = Q/P = 250/Q

From the first two ratios, we can deduce that P^2 = 2Q.

Now, let's look at the third ratio: 250/Q. Since the common ratio applies to all terms, we know that Q/(250/Q) = (Q^2)/250.

Since Q/(250/Q) = Q^2/250, we can set these equal to each other:

Q^2/250 = (Q^2)/250

This implies that Q^2 = 250.

Therefore, the value of Q can be found by taking the square root of 250. In this case, Q has two possible values, positive and negative:

Q = ±√(250) = ± 5√(10).

Now, let's substitute the value of Q back into the equation P^2 = 2Q:

P^2 = 2(± 5√(10)),

which simplifies to:

P^2 = ± 10√(10).

Therefore, the values of P can be found by taking the square root of ± 10√(10). Again, we have two possible values, positive and negative:

P = ±√(± 10√(10)).

In summary, the values of P and Q in the geometric sequence 2, P, Q, 250 are:

Q = ± 5√(10),

P = ±√(± 10√(10)).