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If
a_(1)=4,a_(2)=2 and
a_(n)=2a_(n-1)+a_(n-2) then find the value of
a_(6).
Answer:

If $a_{1}=4, a_{2}=2$ and $a_{n}=2 a_{n-1}+a_{n-2}$ then find the value of $a_{6}$ . $\newline$ Answer:

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Write and solve direct variation equations

Full solution

Q. If

a_{1}=4, a_{2}=2

and

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

then find the value of

a_{6}

.

\newline

Answer:

Understand recursive formula: Understand the recursive formula and initial conditions. $\newline$ The recursive formula given is $a_{n}=2a_{n-1}+a_{n-2}$ , which means each term is the sum of twice the previous term and the term before that. We are given $a_{1}=4$ and $a_{2}=2$ as initial conditions.
Find $a_{3}$ : Find $a_{3}$ using the recursive formula. $\newline$ $a_{3} = 2a_{2} + a_{1}(\newline$ = 2\times 2 + 4(\newline\) = 4 + 4(\newline\) = 8\)
Find $a_{4}$ : Find $a_{4}$ using the recursive formula. $a_{4} = 2a_{3} + a_{2}$ $= 2\times 8 + 2$ $= 16 + 2$ $= 18$
Find $a_{5}$ : Find $a_{5}$ using the recursive formula. $a_{5} = 2a_{4} + a_{3}$ $= 2\times18 + 8$ $= 36 + 8$ $= 44$
Find $a_{6}$ : Find $a_{6}$ using the recursive formula. $\newline$ $a_{6} = 2a_{5} + a_{4}(\newline$ = 2\times44 + 18(\newline\) = 88 + 18(\newline\) = 106\)

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