A sequence $\{u_n\}$ of numbers are defined by $u_1 = 1$ and \[u_{n+1} = 2u_n + 4, \quad n \in \

Question

A sequence $\{u_n\}$ of numbers are defined by $u_1 = 1$ and $$u_{n+1} = 2u_n + 4, \quad n \in \mathbb{N}.$$ Find the values of $u_2, u_3$ and $u_4$. Using GDC, find the least integral value of $n$ for which $u_n > 256$.

Accepted Answer

(i) $u_2=6,\ u_3=16,\ u_4=36$ (ii) $n=7$

Recurrence relation: linear

Recurrence relation: linear

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