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

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

and

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

then find the value of

a_{5}

.

\newline

Answer:

Identify Given Terms and Formula: Identify the given terms of the sequence and the recursive formula. $\newline$ We are given $a_{1}=2$ , $a_{2}=0$ , and the recursive formula $a_{n}=2a_{n-1}-3a_{n-2}$ .
Find $a_{3}$ : Use the recursive formula to find $a_{3}$ . $a_{3} = 2a_{2} - 3a_{1}$ $a_{3} = 2(0) - 3(2)$ $a_{3} = 0 - 6$ $a_{3} = -6$
Find $a_{4}$ : Use the recursive formula to find $a_{4}$ . $\newline$ $a_{4} = 2a_{3} - 3a_{2}$ $\newline$ $a_{4} = 2(-6) - 3(0)$ $\newline$ $a_{4} = -12 - 0$ $\newline$ $a_{4} = -12$
Find $a_{5}$ : Use the recursive formula to find $a_{5}$ .
$a_{5} = 2a_{4} - 3a_{3}$
$a_{5} = 2(-12) - 3(-6)$
$a_{5} = -24 + 18$
$a_{5} = -6$

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