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

Identify Given Terms and Formula: Identify the given terms of the sequence and the recursive formula. 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). a_(3) = 3a_(2) - 2a_(1) a_(3) = 3(1) - 2(3) a_(3) = 3 - 6 a_(3) = -3Find 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) = -11Find 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

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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:

View step-by-step help

Home

Math Problems

Grade 8

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 $a_{5}$ .
$a_{5} = 3a_{4} - 2a_{3}$
$a_{5} = 3(-11) - 2(-3)$
$a_{5} = -33 + 6$
$a_{5} = -27$