If a_(1)=8 and a_(n)=-5a_(n-1)-3 then find the value of a_(5). Answer:

Initialize and Calculate a_(2): To find the value of a_(5), we need to use the recursive formula a_(n)=-5a_(n-1)-3, starting with the given initial condition a_(1)=8.Calculate a_(3): First, we find a_(2) using the initial condition a_(1)=8. a_(2) = -5a_(1) - 3 = -5(8) - 3 = -40 - 3 = -43.Calculate a_(4): Next, we find a_(3) using the value of a_(2). a_(3) = -5a_(2) - 3 = -5(-43) - 3 = 215 - 3 = 212.Calculate a_(5): Then, we find a_(4) using the value of a_(3). a_(4) = -5a_(3) - 3 = -5(212) - 3 = -1060 - 3 = -1063.Finally, we find a_(5) using the value of a_(4). a_(5) = -5a_(4) - 3 = -5(-1063) - 3 = 5315 - 3 = 5312.

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Precalculus

Find the roots of factored polynomials

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Q. If

a_{1}=8

and

a_{n}=-5 a_{n-1}-3

then find the value of

a_{5}

\newline

Answer:

Initialize and Calculate $a_{2}$ : To find the value of $a_{5}$ , we need to use the recursive formula $a_{n}=-5a_{n-1}-3$ , starting with the given initial condition $a_{1}=8$ .
Calculate $a_{3}$ : First, we find $a_{2}$ using the initial condition $a_{1}=8$ . $\newline$ a_{$2$} = $-5$a_{$1$} - $3$ = $-5$($8$) - $3$ = $-40$ - $3$ = $-43$.
Calculate $a_{4}$: Next, we find $a_{3}$ using the value of $a_{2}$. $\newline$a_{ $3$ } = $-5$ a_{ $2$ } - $3$ = $-5$ ( $-43$ ) - $3$ = $215$ - $3$ = $212$ .
Calculate $a_{5}$ : Then, we find $a_{4}$ using the value of $a_{3}$ . $\newline$ $a_{$4$} = $-5$a_{$3$} - $3$ = $-5$($212$) - $3$ = $-1060$ - $3$ = $-1063$.
Calculate $a_{5}$: Then, we find $a_{4}$ using the value of $a_{3}$.$a_{4} = -5a_{3} - 3 = -5(212) - 3 = -1060 - 3 = -1063$.Finally, we find $a_{5}$ using the value of $a_{4}$.$a_{5} = -5a_{4} - 3 = -5(-1063) - 3 = 5315 - 3 = 5312$.