The second term in a geometric sequence is 50. The fourth term in the same sequence is 112.5. What is the common ratio in this sequence?

Question

Casey Rivers

Mathematics

6 February, 04:42

The second term in a geometric sequence is 50. The fourth term in the same sequence is 112.5. What is the common ratio in this sequence?

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Answers (1)

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Jacobson · Answer 1

Geometric an = ar^ (n - 1)

Second term = ar² ⁻ ¹ = ar = 50

Fourth term = ar⁴ ⁻ ¹ = ar³ = 112.5

ar = 50 ... (a)

ar³ = 112.5 ... (b)

Equation (b) / (a)

ar³ / ar = 112.5/50

r² = 2.25

r = √2.25

r = 1.5

Common ratio = 1.5