Mathegoras

Sequences and series › Recursive sequences › Computing terms of a recurrence

First term of a recurrence with a constant subtraction

Middle school · ●●○○○ 20 pts

A sequence a1,a2,a3,…a_1, a_2, a_3, \ldots satisfies an=3an−1−xa_n = 3a_{n-1} - x for every n≥2n \ge 2, where xx is an integer that is the same for all terms. Given that a2=7a_2 = 7 and a4=43a_4 = 43, find a1a_1.

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recurrence relationslinear recurrencessequenceslinear equationssubstitution