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

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3

answer: 0

step-by-step explanation: the positive, like 5, + its opposite, like -5 would be 0

5+(-5)=0, or 5-5=0