Question

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.

Answer 1

Answer:

± 60

Step-by-step explanation:

aₙ = a₁ * rⁿ⁻¹

a₇ = 30 = a₁ * r⁷⁻¹ = a₁ * r⁶     (1)

a₅ = 120 = a₁ * r⁵⁻¹ = a₁ * r⁴     (2)

(1)/(2): 30/120 = 1/4 = r²

r = ± 1/2   or ± 0.5

a₁ = a₇/r⁶ = 30/0.5⁶ = 1920

a₆ = 1920 * (± 1/2)⁶⁻¹ = 1920 * ± 1/32 = ± 60