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

Understand Recursive Formula: Understand the recursive formula and initial conditions. 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. Using the formula a_(n)=2a_(n-1)+a_(n-2), we substitute n=3 to find a_(3). a_(3) = 2a_(2) + a_(1) a_(3) = 2*5 + 4 a_(3) = 10 + 4 a_(3) = 14Find 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*14 + 5 a_(4) = 28 + 5 a_(4) = 33

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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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Math Problems

Grade 8

Write and solve direct variation equations

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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 $n=4$ . $a_4 = 2a_3 + a_2$ $a_4 = 2\times14 + 5$ $a_4 = 28 + 5$ $a_4 = 33$