A sequence $u_1, u_2, u_3, \ldots$ is defined by $u_1=a,$ $u_{r+1}=3u_r+5, r\geqslant 1,$ wher

Question

A sequence $u_1, u_2, u_3, \ldots$ is defined by $u_1=a,$ $u_{r+1}=3u_r+5, r\geqslant 1,$ where $a$ is a constant. Find expressions for $u_2$ and $u_3$ in terms of $a$.[2] It is given that $\displaystyle\sum_{r=1}^{4}u_r=110$. Find the value of $a$.[3]

Accepted Answer

(a) $u_2=3a+5$, $u_3=9a+20$ (b) $a=\dfrac12$

N2025 P1 Q1

N2025 P1 Q1

Video Solution:

Solution 1