A sequence u_n is defined by u_1=5 and u_n+1=2u_n+3 for n in Z+. Prove that u_n=2n+2-3.

Closed Form of a Recurrence

IB Year 5 | Grade 11

A sequence \(\{u_n\}\) is defined by \(u_1=5\) and \(u_{n+1}=2u_n+3\) for \(n\in\mathbb Z^+\). Prove that \(u_n=2^{n+2}-3\).

Video solution locked

A free account saves your progress; this video needs tuition enrolment.

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.

Create a free account to practise similar questions.

Answer:\(u_n=2^{n+2}-3\)

Need help? Join our JC Math tuition classes.