csat-suneung 2012 Q5

csat-suneung · South-Korea · csat__math-humanities 3 marks Arithmetic Sequences and Series Sequence Defined by Recurrence with AP Connection

For a sequence $\left\{ a _ { n } \right\}$ with $a _ { 1 } = 1$ and satisfying
$$a _ { n + 1 } = \frac { 2 n } { n + 1 } a _ { n }$$
for all natural numbers $n$, what is the value of $a _ { 4 }$? [3 points]
(1) $\frac { 3 } { 2 }$
(2) 2
(3) $\frac { 5 } { 2 }$
(4) 3
(5) $\frac { 7 } { 2 }$

For a sequence $\left\{ a _ { n } \right\}$ with $a _ { 1 } = 1$ and satisfying

$$a _ { n + 1 } = \frac { 2 n } { n + 1 } a _ { n }$$

for all natural numbers $n$, what is the value of $a _ { 4 }$? [3 points]\\
(1) $\frac { 3 } { 2 }$\\
(2) 2\\
(3) $\frac { 5 } { 2 }$\\
(4) 3\\
(5) $\frac { 7 } { 2 }$

Paper Questions

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