The 5th term in a geometric sequence is 120. the 7th term is 30 what are the possible values of the 6th term of the sequence? a. 60 b. ±60 c. 75 d. ±75

b. ± 60

Step-by-step explanation:

Let the geometric series is,

Where, a is the first term and r be the common ratio,

Given,

5th term in a geometric sequence is 120.

Also, 7th term is 30,

Equation (2) / Equation (1),

Now, r × Equation (1),

Case 1 :

When r = 1/2

Case 2 :

When r = -1/2

Hence,  the possible values of the 6th term of the sequence is ± 60

Option b is correct.

Alternative method :

Since, 6th term of sequence is between the 5th term and 7th term,

Thus, the 6th term = Geometric mean of 5th term and 7th term

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.