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

Question

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}Find the exact value of $l$, given that when $n	o \infty $, ${{x}_{n}}	o l$. Show that ${{x}_{n+1}}^{2}-{{l}^{2}}=3\left( {{x}_{n}}-l ight)$. Show algebraically that if ${{x}_{n}} \lt l $ for some value of $n$, then ${{x}_{n+1}} \gt l$.

Accepted Answer

(i) $-\frac83l$.

Limit of a Sequence and Behaviour of a Sequence Q1

Limit of a Sequence and Behaviour of a Sequence Q1

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