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

Understand recursive formula: Understand the recursive formula and initial conditions. 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. a_(3) = a_(2) + 3a_(1) Substitute the given values: a_(3) = 0 + 3*5 Calculate a_(3): a_(3) = 15Find a_(4): Find a_(4) using the recursive formula. a_(4) = a_(3) + 3a_(2) Substitute the values found: a_(4) = 15 + 3*0 Calculate a_(4): a_(4) = 15Find a_(5): Find a_(5) using the recursive formula. a_(5) = a_(4) + 3a_(3) Substitute the values found: a_(5) = 15 + 3*15 Calculate a_(5): a_(5) = 15 + 45 Calculate a_(5): a_(5) = 60

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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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Math Problems

Grade 8

Write and solve direct variation equations

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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 $a_{5}$ : $a_{5} = 60$