Word Count : 417

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Let's break down and solve each part of the problem step by step: ### Part (a): Find a recurrence relation and initial conditions for 4, 14, 44, 134, 404, ... The given sequence is: \[ 4, 14, 44, 134, 404, \dots \] First, let's examine the differences between successive terms to look for a pattern: - \( 14 - 4 = 10 \) - \( 44 - 14 = 30 \) - \( 134 - 44 = 90 \) - \( 404 - __________ ________ ________ __________ _______ ______ ____.
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