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Question Number 199709 by tri26112004 last updated on 08/Nov/23

u_1 = 2 u_(n+1) = 3u_n + 2 u_n → n ¿

u1=2un+1=3un+2un→n¿

Answered by mr W last updated on 08/Nov/23

u_(n+1) +1=3u_n +2+1=3(u_n +1) u_n +1=3(u_(n−1) +1)=3^2 (u_(n−2) +1)=...=3^(n−1) (u_1 +1)=3^(n−1) (2+1)=3^n ⇒u_n =3^n −1

un+1+1=3un+2+1=3(un+1)un+1=3(un−1+1)=32(un−2+1)=...=3n−1(u1+1)=3n−1(2+1)=3n⇒un=3n−1

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