The possible values of the 6th term of the sequence ± 60.
The 5th term in a geometric sequence is 120.
The 7th term is 30
We have to determine the 6th term of the sequence.
What is the formula for the nth term of the sequence?
[tex]a_n = a* r^n[/tex]
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.
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