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Home » Difference: 252 – 225 = 27 - 500apps

Difference: 252 – 225 = <<252-225=27>>27 - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 A geometric sequence has a first term of 3 and a common ratio of 2. What is the 6th term in the sequence?

📌 The \(n\)-th term of a geometric sequence is given by \(a_n = a_1 \cdot r^{(n-1)}\).

📌 For the 6th term: \(a_6 = 3 \cdot 2^{(6-1)} = 3 \cdot 2^5 = 3 \cdot 32 = 96\).

📌 Solve for \(x\) in the equation: \(2^{3x} = 64\).

📌 Express 64 as a power of 2: \(64 = 2^6\).

📌 Thus, \(2^{3x} = 2^6\).

📌 Set the exponents equal: \(3x = 6\).

📌 Solve for \(x\): \(x = rac{6}{3} = 2\).

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