A sequence ${{u}_{1}},{{u}_{2}},{{u}_{3}},\ldots $ is such that ${{u}_{1}}=2$, ${{u}_{n+1}}=\frac{{{

Question

A sequence ${{u}_{1}},{{u}_{2}},{{u}_{3}},\ldots $ is such that ${{u}_{1}}=2$, ${{u}_{n+1}}=\frac{{{u}_{n}}}{5}-3$ for all $n\ge 1$, where $k$ is a constant. Write down the values of ${{u}_{2}}$, ${{u}_{3}}$ and ${{u}_{4}}$. [2] Given that the sequence converges to $l$, find the value of $l$. [1]

Accepted Answer

(i) u₂=-13/5, u₃=-88/25, u₄=-463/125; (ii) l=-15/4

RI Sequences and Series tutorial 7A Q4

RI Sequences and Series tutorial 7A Q4

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