If a_(1)=9 and a_(n)=na_(n-1)+4 then find the value of a_(4). Answer:

Given Information: We are given the first term of the sequence, a_(1)=9, and a recursive formula for the nth term: a_(n)=na_(n-1)+4. To find a_(4), we need to find the values of a_(2), a_(3), and then a_(4) using the recursive formula.Find a_(2): First, let's find a_(2) using the recursive formula. We know that a_(1)=9, so we substitute n=2 and a_(1)=9 into the formula to get a_(2)=2*a_(1)+4. Calculation: a_(2)=2*9+4=18+4=22.Find a_(3): Next, we find a_(3) using the recursive formula. We now know that a_(2)=22, so we substitute n=3 and a_(2)=22 into the formula to get a_(3)=3*a_(2)+4. Calculation: a_(3)=3*22+4=66+4=70.Find a_(4): Finally, we find a_(4) using the recursive formula. We know that a_(3)=70, so we substitute n=4 and a_(3)=70 into the formula to get a_(4)=4*a_(3)+4. Calculation: a_(4)=4*70+4=280+4=284.

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Precalculus

Find the roots of factored polynomials

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Q. If

a_{1}=9

and

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

then find the value of

a_{4}

\newline

Answer:

Given Information: We are given the first term of the sequence, $a_{1}=9$ , and a recursive formula for the $n$ th term: $a_{n}=na_{n-1}+4$ . To find $a_{4}$ , we need to find the values of $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula.
Find $a_{2}$ : First, let's find $a_{2}$ using the recursive formula. We know that $a_{1}=9$ , so we substitute $n=2$ and $a_{1}=9$ into the formula to get $a_{2}=2\cdot a_{1}+4$ . $\newline$ Calculation: $a_{2}=2\cdot 9+4=18+4=22$ .
Find $a_{3}$ : Next, we find $a_{3}$ using the recursive formula. We now know that $a_{2}=22$ , so we substitute $n=3$ and $a_{2}=22$ into the formula to get $a_{3}=3\cdot a_{2}+4$ . $\newline$ Calculation: $a_{3}=3\cdot 22+4=66+4=70$ .
Find $a_{4}$ : Finally, we find $a_{4}$ using the recursive formula. We know that $a_{3}=70$ , so we substitute $n=4$ and $a_{3}=70$ into the formula to get $a_{4}=4\cdot a_{3}+4$ . $\newline$ Calculation: $a_{4}=4\cdot 70+4=280+4=284$ .