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

Calculate a_(2): To find a_(4), we need to use the recursive formula a_(n)=na_(n-1)+4, starting with the given a_(1)=6. First, we find a_(2) using the formula with n=2. a_(2) = 2 * a_(1) + 4 = 2 * 6 + 4 = 12 + 4 = 16Calculate a_(3): Next, we find a_(3) using the formula with n=3 and the previously found value of a_(2). a_(3) = 3 * a_(2) + 4 = 3 * 16 + 4 = 48 + 4 = 52Calculate a_(4): Finally, we find a_(4) using the formula with n=4 and the previously found value of a_(3). a_(4) = 4 * a_(3) + 4 = 4 * 52 + 4 = 208 + 4 = 212

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

View step-by-step help

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=6

and

a_{n}=n a_{n-1}+4

then find the value of

a_{4}

\newline

Answer:

Calculate $a_{2}$ : To find $a_{4}$ , we need to use the recursive formula $a_{n}=na_{n-1}+4$ , starting with the given $a_{1}=6$ . First, we find $a_{2}$ using the formula with $n=2$ . $a_{2} = 2 \cdot a_{1} + 4$ $= 2 \cdot 6 + 4$ $= 12 + 4$ $= 16$
Calculate $a_{3}$ : Next, we find $a_{3}$ using the formula with $n=3$ and the previously found value of $a_{2}$ .
$a_{3} = 3 \times a_{2} + 4$
$\phantom{a_{3}} = 3 \times 16 + 4$
$\phantom{a_{3}} = 48 + 4$
$\phantom{a_{3}} = 52$
Calculate $a_{4}$ : Finally, we find $a_{4}$ using the formula with $n=4$ and the previously found value of $a_{3}$ . $\newline$ $a_{4} = 4 \times a_{3} + 4$ $\newline$ $= 4 \times 52 + 4$ $\newline$ $= 208 + 4$ $\newline$ $= 212$