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traducere romana engleza - DevRocket

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Consider the sequence defined by the recursive formula \( a_n = 2a_{n-1} - 3 \) with the initial term \( a_1 = 4 \). Find the explicit formula for the \( n \)-th term of the sequence.

📌 To find the explicit formula, we first solve the homogeneous part of the recurrence relation \( a_n = 2a_{n-1} \), which gives \( a_n = C \cdot 2^n \) for some constant \( C \). Next, we find a particular solution for the non-homogeneous recurrence. Trying a constant solution \( a_n = A \):

📌 A = 2A - 3 \im

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