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

Understand the formula: Understand the recursive formula and initial conditions. The recursive formula given is a_(n)=2a_(n-1)+a_(n-2), which means each term is the sum of twice the previous term and the term before that. We are given a_(1)=2 and a_(2)=1.Find a_(3): Find the value of a_(3) using the recursive formula. a_(3) = 2a_(2) + a_(1) a_(3) = 2(1) + 2 a_(3) = 2 + 2 a_(3) = 4Find a_(4): Find the value of a_(4) using the recursive formula. a_(4) = 2a_(3) + a_(2) a_(4) = 2(4) + 1 a_(4) = 8 + 1 a_(4) = 9Find a_(5): Find the value of a_(5) using the recursive formula. a_(5) = 2a_(4) + a_(3) a_(5) = 2(9) + 4 a_(5) = 18 + 4 a_(5) = 22

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

and

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

then find the value of

a_{5}

\newline

Answer:

Understand the formula: Understand the recursive formula and initial conditions. $\newline$ The recursive formula given is $a_{n}=2a_{n-1}+a_{n-2}$ , which means each term is the sum of twice the previous term and the term before that. We are given $a_{1}=2$ and $a_{2}=1$ .
Find $a_{3}$ : Find the value of $a_{3}$ using the recursive formula. $a_{3} = 2a_{2} + a_{1}$ $a_{3} = 2(1) + 2$ $a_{3} = 2 + 2$ $a_{3} = 4$
Find $a_{4}$ : Find the value of $a_{4}$ using the recursive formula. $a_{4} = 2a_{3} + a_{2}$ $a_{4} = 2(4) + 1$ $a_{4} = 8 + 1$ $a_{4} = 9$
Find $a_{5}$ : Find the value of $a_{5}$ using the recursive formula. $\newline$ $a_{5} = 2a_{4} + a_{3}$ $\newline$ $a_{5} = 2(9) + 4$ $\newline$ $a_{5} = 18 + 4$ $\newline$ $a_{5} = 22$