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

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this