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If
a_(1)=2,a_(2)=1 and
a_(n)=2a_(n-1)+a_(n-2) then find the value of
a_(5).
Answer:

If $a_{1}=2, a_{2}=1$ and $a_{n}=2 a_{n-1}+a_{n-2}$ then find the value of $a_{5}$ . $\newline$ Answer:

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Write and solve direct variation equations

Full solution

Q. If

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

and

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

then find the value of

a_{5}

.

\newline

Answer:

Understand the 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 $a_{1}=2$ and $a_{2}=1$ .
Find $a_{3}$ : Find the value of $a_{3}$ using the recursive formula. $a_{3} = 2a_{2} + a_{1}$ $a_{3} = 2(1) + 2$ $a_{3} = 2 + 2$ $a_{3} = 4$
Find $a_{4}$ : Find the value of $a_{4}$ using the recursive formula. $a_{4} = 2a_{3} + a_{2}$ $a_{4} = 2(4) + 1$ $a_{4} = 8 + 1$ $a_{4} = 9$
Find $a_{5}$ : Find the value of $a_{5}$ using the recursive formula. $\newline$ $a_{5} = 2a_{4} + a_{3}$ $\newline$ $a_{5} = 2(9) + 4$ $\newline$ $a_{5} = 18 + 4$ $\newline$ $a_{5} = 22$

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