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ValentinkaMS [17]
3 years ago
15

What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54, respectively?

Mathematics
2 answers:
Maslowich3 years ago
7 0
A₂ = 6      a₄ = 54

a_{n}  =  q^{n-1}  *  a_{1} 

\left \{ {{ a_{2} = q^{2-1} * a_{1} } \atop { a_{4} = q^{4-1}* a_{1}  }} \right.   \\  \\  \left \{ {{6 = q *  a_{1} } \atop {54 =  q^{3} *  a_{1}  }} \right.   \\  \\   \left \{ {{  a_{1} = \frac{6}{q} } \atop {54 = q^{3} * \frac{6}{q}  }} \right.  \\  \\   \left \{ {{ a_{1}  =  \frac{6}{q} } \atop {54 =  q^{2} * 6 }} \right. 

\left \{ {{ a_{1} =  \frac{6}{q} } \atop { q^{2} =9}} \right.  \\  \\  \left \{ {{ a_{1} = \frac{6}{q} } \atop {q= \sqrt{9} }} \right. 
 
q = 3     q = -3

a₁ = 6/3 = 2   a₁ = 6/-3 = -2
Lemur [1.5K]3 years ago
5 0
Hi there! T4=T2×r²,6r²=54. Therefore, the answer would be 3.
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