If a_(1)=4,a_(2)=2 and a_(n)=2a_(n-1)+a_(n-2) then find the value of a_(6). Answer:

Understand recursive 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)=4 and a_(2)=2 as initial conditions.Find a_(3): Find a_(3) using the recursive formula. a_(3) = 2a_(2) + a_(1) = 2*2 + 4 = 4 + 4 = 8Find a_(4): Find a_(4) using the recursive formula. a_(4) = 2a_(3) + a_(2) = 2*8 + 2 = 16 + 2 = 18Find a_(5): Find a_(5) using the recursive formula. a_(5) = 2a_(4) + a_(3) = 2*18 + 8 = 36 + 8 = 44Find a_(6): Find a_(6) using the recursive formula. a_(6) = 2a_(5) + a_(4) = 2*44 + 18 = 88 + 18 = 106

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
a_(1)=4,a_(2)=2 and
a_(n)=2a_(n-1)+a_(n-2) then find the value of
a_(6).
Answer:

If $a_{1}=4, a_{2}=2$ and $a_{n}=2 a_{n-1}+a_{n-2}$ then find the value of $a_{6}$ . $\newline$ Answer:

View step-by-step help

Home

Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

a_{1}=4, a_{2}=2

and

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

then find the value of

a_{6}

\newline

Answer:

Understand recursive 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 $a_{1}=4$ and $a_{2}=2$ as initial conditions.
Find $a_{3}$ : Find $a_{3}$ using the recursive formula. $\newline$ $a_{3} = 2a_{2} + a_{1}(\newline$ = 2\times 2 + 4(\newline\) = 4 + 4(\newline\) = 8\)
Find $a_{4}$ : Find $a_{4}$ using the recursive formula. $a_{4} = 2a_{3} + a_{2}$ $= 2\times 8 + 2$ $= 16 + 2$ $= 18$
Find $a_{5}$ : Find $a_{5}$ using the recursive formula. $a_{5} = 2a_{4} + a_{3}$ $= 2\times18 + 8$ $= 36 + 8$ $= 44$
Find $a_{6}$ : Find $a_{6}$ using the recursive formula. $\newline$ $a_{6} = 2a_{5} + a_{4}(\newline$ = 2\times44 + 18(\newline\) = 88 + 18(\newline\) = 106\)