If a_(1)=0,a_(2)=3 and a_(n)=3a_(n-1)-a_(n-2) then find the value of a_(4). Answer:

Find a_(3): Use the given recursive formula to find a_(3). The recursive formula is a_(n)=3a_(n-1)-a_(n-2). We know a_(1)=0 and a_(2)=3. Substitute n=3 into the formula to find a_(3). a_(3) = 3a_(3-1) - a_(3-2) a_(3) = 3a_(2) - a_(1) a_(3) = 3*3 - 0 a_(3) = 9 - 0 a_(3) = 9Find a_(4): Use the recursive formula to find a_(4). Now that we have a_(3), we can use the formula again to find a_(4). a_(4) = 3a_(4-1) - a_(4-2) a_(4) = 3a_(3) - a_(2) a_(4) = 3*9 - 3 a_(4) = 27 - 3 a_(4) = 24

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
a_(1)=0,a_(2)=3 and
a_(n)=3a_(n-1)-a_(n-2) then find the value of
a_(4).
Answer:

If $a_{1}=0, a_{2}=3$ and $a_{n}=3 a_{n-1}-a_{n-2}$ then find the value of $a_{4}$ . $\newline$ Answer:

View step-by-step help

Home

Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

a_{1}=0, a_{2}=3

and

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

then find the value of

a_{4}

\newline

Answer:

Find $a_{3}$ : Use the given recursive formula to find $a_{3}$ . The recursive formula is $a_{n}=3a_{n-1}-a_{n-2}$ . We know $a_{1}=0$ and $a_{2}=3$ . Substitute $n=3$ into the formula to find $a_{3}$ . $a_{3} = 3a_{3-1} - a_{3-2}$ $a_{3} = 3a_{2} - a_{1}$ $a_{3} = 3\times3 - 0$ $a_{3}$ $0$ $a_{3}$ $1$
Find $a_{4}$ : Use the recursive formula to find $a_{4}$ . Now that we have $a_{3}$ , we can use the formula again to find $a_{4}$ . $a_{4} = 3a_{4-1} - a_{4-2}$ $a_{4} = 3a_{3} - a_{2}$ $a_{4} = 3\times9 - 3$ $a_{4} = 27 - 3$ $a_{4} = 24$