For the following sequence, write down their ${{2}^{\mathrm{nd}}}$ and ${{3}^{\mathrm{rd}}}$ terms,

Question

For the following sequence, write down their ${{2}^{\mathrm{nd}}}$ and ${{3}^{\mathrm{rd}}}$ terms, and determine whether the sequences are convergent. If they are, write down their limits. ${{u}_{1}}=-2$, ${{u}_{n+1}}=-\frac{1}{2}{{u}_{n}}$ for $n\ge 1$ ${{u}_{1}}=3$, $2{{u}_{n}}={{u}_{n-1}}-4$, for $n\ge 2$ ${{u}_{1}}=1$, ${{u}_{n+1}}=2{{u}_{n}}-1$, for $n\ge 1$ ${{u}_{1}}=2$, ${{u}_{n+1}}=2{{u}_{n}}-1$, for $n\ge 1$

Accepted Answer

(i) $u_2=1,\ u_3=-\frac12$, limit $0$ (ii) $u_2=-\frac12,\ u_3=-\frac94$, limit $-4$ (iii) $u_2=u_3=1$, limit $1$ (iv) $u_2=3,\ u_3=5$, divergent

2024 ACJC Recurrence Relations Tutorial Q5

2024 ACJC Recurrence Relations Tutorial Q5

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