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

Initialize Recursive Formula: To find a_(5), we need to use the recursive formula a_(n)=a_(n-1)+2a_(n-2) to find the values of a_(3), a_(4), and then a_(5). We already know a_(1)=3 and a_(2)=2.Calculate a_(3): Let's calculate a_(3) using the recursive formula: a_(3)=a_(3-1)+2a_(3-2) which simplifies to a_(3)=a_(2)+2a_(1).Calculate a_(4): Substitute the known values into the formula: a_(3)=2+2*3 which simplifies to a_(3)=2+6.Calculate a_(5): Calculate the value of a_(3): a_(3)=8.Now let's calculate a_(4) using the recursive formula: a_(4)=a_(4-1)+2a_(4-2) which simplifies to a_(4)=a_(3)+2a_(2).Substitute the known values into the formula: a_(4)=8+2*2 which simplifies to a_(4)=8+4.Calculate the value of a_(4): a_(4)=12.Finally, let's calculate a_(5) using the recursive formula: a_(5)=a_(5-1)+2a_(5-2) which simplifies to a_(5)=a_(4)+2a_(3).Substitute the known values into the formula: a_(5)=12+2*8 which simplifies to a_(5)=12+16.Calculate the value of a_(5): a_(5)=28.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

If $a_{1}=3, a_{2}=2$ and $a_{n}=a_{n-1}+2 a_{n-2}$ then find the value of $a_{5}$ . $\newline$ Answer:

View step-by-step help

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

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

and

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

then find the value of

a_{5}

\newline

Answer:

Initialize Recursive Formula: To find $a_{5}$ , we need to use the recursive formula $a_{n}=a_{n-1}+2a_{n-2}$ to find the values of $a_{3}$ , $a_{4}$ , and then $a_{5}$ . We already know $a_{1}=3$ and $a_{2}=2$ .
Calculate $a_{3}$ : Let's calculate $a_{3}$ using the recursive formula: $a_{3}=a_{3-1}+2a_{3-2}$ which simplifies to $a_{3}=a_{2}+2a_{1}$ .
Calculate $a_{4}$ : Substitute the known values into the formula: $a_{3}=2+2\times 3$ which simplifies to $a_{3}=2+6$ .
Calculate $a_{5}$ : Calculate the value of $a_{3}$ : $a_{3}=8$ .
Calculate $a_{5}$ : Calculate the value of $a_{3}$ : $a_{3}=8$ .Now let's calculate $a_{4}$ using the recursive formula: $a_{4}=a_{4-1}+2a_{4-2}$ which simplifies to $a_{4}=a_{3}+2a_{2}$ .
Calculate $a_{5}$ : Calculate the value of $a_{3}$ : $a_{3}=8$ .Now let's calculate $a_{4}$ using the recursive formula: $a_{4}=a_{4-1}+2a_{4-2}$ which simplifies to $a_{4}=a_{3}+2a_{2}$ .Substitute the known values into the formula: $a_{4}=8+2\times 2$ which simplifies to $a_{4}=8+4$ .
Calculate $a_{5}$ : Calculate the value of $a_{3}$ : $a_{3}=8$ .Now let's calculate $a_{4}$ using the recursive formula: $a_{4}=a_{4-1}+2a_{4-2}$ which simplifies to $a_{4}=a_{3}+2a_{2}$ .Substitute the known values into the formula: $a_{4}=8+2\times 2$ which simplifies to $a_{4}=8+4$ .Calculate the value of $a_{4}$ : $a_{4}=12$ .
Calculate $a_{5}$ : Calculate the value of $a_{3}$ : $a_{3}=8$ .Now let's calculate $a_{4}$ using the recursive formula: $a_{4}=a_{4-1}+2a_{4-2}$ which simplifies to $a_{4}=a_{3}+2a_{2}$ .Substitute the known values into the formula: $a_{4}=8+2\times 2$ which simplifies to $a_{4}=8+4$ .Calculate the value of $a_{4}$ : $a_{4}=12$ .Finally, let's calculate $a_{5}$ using the recursive formula: $a_{3}$ $1$ which simplifies to $a_{3}$ $2$ .
Calculate $a_{5}$ : Calculate the value of $a_{3}$ : $a_{3}=8$ .Now let's calculate $a_{4}$ using the recursive formula: $a_{4}=a_{4-1}+2a_{4-2}$ which simplifies to $a_{4}=a_{3}+2a_{2}$ .Substitute the known values into the formula: $a_{4}=8+2\times 2$ which simplifies to $a_{4}=8+4$ .Calculate the value of $a_{4}$ : $a_{4}=12$ .Finally, let's calculate $a_{5}$ using the recursive formula: $a_{3}$ $1$ which simplifies to $a_{3}$ $2$ .Substitute the known values into the formula: $a_{3}$ $3$ which simplifies to $a_{3}$ $4$ .
Calculate $a_{5}$ : Calculate the value of $a_{3}$ : $a_{3}=8$ .Now let's calculate $a_{4}$ using the recursive formula: $a_{4}=a_{4-1}+2a_{4-2}$ which simplifies to $a_{4}=a_{3}+2a_{2}$ .Substitute the known values into the formula: $a_{4}=8+2\times 2$ which simplifies to $a_{4}=8+4$ .Calculate the value of $a_{4}$ : $a_{4}=12$ .Finally, let's calculate $a_{5}$ using the recursive formula: $a_{3}$ $1$ which simplifies to $a_{3}$ $2$ .Substitute the known values into the formula: $a_{3}$ $3$ which simplifies to $a_{3}$ $4$ .Calculate the value of $a_{5}$ : $a_{3}$ $6$ .