<p>A sequence of negative numbers is defined by ${{x}_{n+1}}=-\sqrt{8+3{{x}_{n}}}$ for $n=1$, $2$, $3$, …</p>
<ol class="i-list"><li><div class="list-item-paragraph">Show that $-\frac{8}{3}<{{x}_{n}}<0$ for $n=1$, $2$, $3$, …</div></li><li><div class="list-item-paragraph">Find the exact value of $l$, given that when $n\to \infty $, ${{x}_{n}}\to l$.</div></li><li><div class="list-item-paragraph">Show that ${{x}_{n+1}}^{2}-{{l}^{2}}=3\left( {{x}_{n}}-l \right)$.</div></li><li><div class="list-item-paragraph">Show algebraically that if ${{x}_{n}} \lt l $ for some value of $n$, then ${{x}_{n+1}} \gt l$.</div></li></ol>

A sequence of negative numbers is defined by ${{x}_{n+1}}=-\sqrt{8+3{{x}_{n}}}$ for $n=1$, $2$, $3$, …

Show that $-\frac{8}{3}<{{x}_{n}}<0$ for $n=1$, $2$, $3$, …

Find the exact value of $l$, given that when $n\to \infty $, ${{x}_{n}}\to l$.

Show that ${{x}_{n+1}}^{2}-{{l}^{2}}=3\left( {{x}_{n}}-l \right)$.

Show algebraically that if ${{x}_{n}} \lt l $ for some value of $n$, then ${{x}_{n+1}} \gt l$.

Limit of a Sequence and Behaviour of a Sequence

Recurrence Relations and Summation

H2 Math

International Baccalaureate Higher Level Mathematics

Limit of a Sequence and Behaviour of a Sequence Q1

Limit of a Sequence and Behaviour of a Sequence Q1

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