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If
a_(1)=5,a_(2)=0 and
a_(n)=a_(n-1)+3a_(n-2) then find the value of
a_(5).
Answer:

If $a_{1}=5, a_{2}=0$ and $a_{n}=a_{n-1}+3 a_{n-2}$ 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}=5, a_{2}=0

and

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

then find the value of

a_{5}

.

\newline

Answer:

Understand recursive formula: Understand the recursive formula and initial conditions. $\newline$ The recursive formula is given by $a_{n}=a_{n-1}+3a_{n-2}$ . This means that each term in the sequence is the sum of the previous term and three times the term before that. We are given $a_{1}=5$ and $a_{2}=0$ as initial conditions.
Find $a_{3}$ : Find $a_{3}$ using the recursive formula. $\newline$ $a_{3} = a_{2} + 3a_{1}$ $\newline$ Substitute the given values: $a_{3} = 0 + 3\times5$ $\newline$ Calculate $a_{3}$ : $a_{3} = 15$
Find $a_{4}$ : Find $a_{4}$ using the recursive formula. $a_{4} = a_{3} + 3a_{2}$ Substitute the values found: $a_{4} = 15 + 3\times 0$ Calculate $a_{4}$ : $a_{4} = 15$
Find $a_{5}$ : Find $a_{5}$ using the recursive formula. $\newline$ $a_{5} = a_{4} + 3a_{3}$ $\newline$ Substitute the values found: $a_{5} = 15 + 3\times15$ $\newline$ Calculate $a_{5}$ : $a_{5} = 15 + 45$ $\newline$ Calculate $a_{5}$ : $a_{5} = 60$

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