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

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

and

a_{n}=3 a_{n-1}-2 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 $a_{1}=3$ , $a_{2}=1$ , and the recursive formula $a_{n}=3a_{n-1}-2a_{n-2}$ .
Find $a_{3}$ : Use the recursive formula to find $a_{3}$ . $\newline$ $a_{3} = 3a_{2} - 2a_{1}$ $\newline$ $a_{3} = 3(1) - 2(3)$ $\newline$ $a_{3} = 3 - 6$ $\newline$ $a_{3} = -3$
Find $a_{4}$ : Use the recursive formula to find $a_{4}$ .
$a_{4} = 3a_{3} - 2a_{2}$
$a_{4} = 3(-3) - 2(1)$
$a_{4} = -9 - 2$
$a_{4} = -11$
Find $a_{5}$ : Use the recursive formula to find $a_{5}$ .
$a_{5} = 3a_{4} - 2a_{3}$
$a_{5} = 3(-11) - 2(-3)$
$a_{5} = -33 + 6$
$a_{5} = -27$

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