If a_(1)=1 and a_(n)=na_(n-1)+5 then find the value of a_(4). Answer:

Find a_(2): To find a_(4), we need to first find a_(2) using the given recursive formula a_(n)=na_(n-1)+5 with n=2. a_(2) = 2 * a_(1) + 5 Since we know a_(1) = 1, we can substitute it into the equation. a_(2) = 2 * 1 + 5 = 2 + 5 = 7Find a_(3): Now we need to find a_(3) using the recursive formula with n=3. a_(3) = 3 * a_(2) + 5 We have already found a_(2) = 7, so we can substitute it into the equation. a_(3) = 3 * 7 + 5 = 21 + 5 = 26Find a_(4): Finally, we can find a_(4) using the recursive formula with n=4. a_(4) = 4 * a_(3) + 5 We have already found a_(3) = 26, so we can substitute it into the equation. a_(4) = 4 * 26 + 5 = 104 + 5 = 109

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If
a_(1)=1 and
a_(n)=na_(n-1)+5 then find the value of
a_(4).
Answer:

If $a_{1}=1$ and $a_{n}=n a_{n-1}+5$ then find the value of $a_{4}$ . $\newline$ Answer:

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Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=1

and

a_{n}=n a_{n-1}+5

then find the value of

a_{4}

\newline

Answer:

Find $a_{2}$ : To find $a_{4}$ , we need to first find $a_{2}$ using the given recursive formula $a_{n}=na_{n-1}+5$ with $n=2$ . $\newline$ $a_{2} = 2 \times a_{1} + 5$ $\newline$ Since we know $a_{1} = 1$ , we can substitute it into the equation. $\newline$ $a_{2} = 2 \times 1 + 5 = 2 + 5 = 7$
Find $a_{3}$ : Now we need to find $a_{3}$ using the recursive formula with $n=3$ . $\newline$ $a_{3} = 3 \times a_{2} + 5$ $\newline$ We have already found $a_{2} = 7$ , so we can substitute it into the equation. $\newline$ $a_{3} = 3 \times 7 + 5 = 21 + 5 = 26$
Find $a_{4}$ : Finally, we can find $a_{4}$ using the recursive formula with $n=4$ .
$a_{4} = 4 \times a_{3} + 5$
We have already found $a_{3} = 26$ , so we can substitute it into the equation.
$a_{4} = 4 \times 26 + 5 = 104 + 5 = 109$