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If
a_(1)=4,a_(2)=5 and
a_(n)=2a_(n-1)+a_(n-2) then find the value of
a_(4).
Answer:

If $a_{1}=4, a_{2}=5$ and $a_{n}=2 a_{n-1}+a_{n-2}$ then find the value of $a_{4}$ . $\newline$ Answer:

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Write and solve direct variation equations

Full solution

Q. If

a_{1}=4, a_{2}=5

and

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

then find the value of

a_{4}

.

\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 $a_{2}=5$ as initial conditions.
Find $a_{3}$ Value: Find the value of $a_{3}$ using the recursive formula. $\newline$ Using the formula $a_{n}=2a_{n-1}+a_{n-2}$ , we substitute $n=3$ to find $a_{3}$ . $\newline$ $a_{3} = 2a_{2} + a_{1}$ $\newline$ $a_{3} = 2\times 5 + 4$ $\newline$ $a_{3} = 10 + 4$ $\newline$ $a_{3} = 14$
Find $a_4$ Value: Find the value of $a_4$ using the recursive formula and the values of $a_2$ and $a_3$ . Now we use the formula $a_n=2a_{n-1}+a_{n-2}$ with $n=4$ . $a_4 = 2a_3 + a_2$ $a_4 = 2\times14 + 5$ $a_4 = 28 + 5$ $a_4 = 33$

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