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Summation by Sigma Method

The terms of ...

Question

The terms of a sequence are defined by $a_{n} = 3 a_{n - 1} - a_{n - 2}$ for $n > 2$ . Find the value of $a_{5}$ given that $a_{1} = 4$ and $a_{2} = 3$ .

12

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23

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25

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31

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36

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Solution

The correct option is D $31$
Given $a_{n} = 3 a_{n - 1} - a_{n - 2}$ , $a_{1} = 4$ and $a_{2} = 3$
$a_{3} = 3 a_{2} - a_{1} = 9 - 4 = 5$
$a_{4} = 3 a_{3} - a_{2} = 15 - 3 = 12$
$a_{5} = 3 a_{4} - a_{3} = 36 - 5 = 31$

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Similar questions

Find the first four terms of the sequence defined by $a_{1} = 3$ and $a_{n} = 3 a_{n - 1} + 2$ , for all n > 1.

a_{1} = 3, a_{n} = 3 a_{n - 1} + 1

n > 1

{a_{n}}

a_{1} = 2

a_{n} = \frac{a_{n - 1}^{2}}{a_{n - 2}}

n \geq 3

a_{2}

a_{5}

a_{5} \leq 162

a_{5}

a_{1} = 0

a_{2} = 1

n > 2

a_{n} = a_{n - 1} - 3 a_{n - 2}

a_{6}

(a_{n})

a_{1} = 2

a_{n} = \frac{a_{n - 1}^{2}}{a_{n - 2}}

n \geq 3

a_{1}

a_{5}

a_{5} \leq 162

a_{5}

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