If a_(1)=9 and a_(n)=-2a_(n-1)-4 then find the value of a_(5). Answer:

Given Information: We are given the first term of the sequence, a_(1)=9, and a recursive formula for the sequence: a_(n)=-2a_(n-1)-4. To find a_(5), we need to find the values of a_(2), a_(3), and a_(4) first, using the recursive formula.Find a_(2): Let's find a_(2) using the recursive formula: a_(2)=-2a_(1)-4. Substitute a_(1)=9 into the formula: a_(2)=-2*9-4=-18-4=-22.Find a_(3): Now, let's find a_(3) using the recursive formula: a_(3)=-2a_(2)-4. Substitute a_(2)=-22 into the formula: a_(3)=-2*(-22)-4=44-4=40.Find a_(4): Next, we find a_(4) using the recursive formula: a_(4)=-2a_(3)-4. Substitute a_(3)=40 into the formula: a_(4)=-2*40-4=-80-4=-84.Find a_(5): Finally, we find a_(5) using the recursive formula: a_(5)=-2a_(4)-4. Substitute a_(4)=-84 into the formula: a_(5)=-2*(-84)-4=168-4=164.

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Find the roots of factored polynomials

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Q. If

a_{1}=9

and

a_{n}=-2 a_{n-1}-4

then find the value of

a_{5}

\newline

Answer:

Given Information: We are given the first term of the sequence, $a_{1}=9$ , and a recursive formula for the sequence: $a_{n}=-2a_{n-1}-4$ . To find $a_{5}$ , we need to find the values of $a_{2}$ , $a_{3}$ , and $a_{4}$ first, using the recursive formula.
Find $a_{2}$ : Let's find $a_{2}$ using the recursive formula: $a_{2}=-2a_{1}-4$ . Substitute $a_{1}=9$ into the formula: $a_{2}=-2\times 9-4=-18-4=-22$ .
Find $a_{3}$ : Now, let's find $a_{3}$ using the recursive formula: $a_{3}=-2a_{2}-4$ . Substitute $a_{2}=-22$ into the formula: $a_{3}=-2*(-22)-4=44-4=40$ .
Find $a_{4}$ : Next, we find $a_{4}$ using the recursive formula: $a_{4}=-2a_{3}-4$ . Substitute $a_{3}=40$ into the formula: $a_{4}=-2\times 40-4=-80-4=-84$ .
Find $a_{5}$ : Finally, we find $a_{5}$ using the recursive formula: $a_{5}=-2a_{4}-4$ . $\newline$ Substitute $a_{4}=-84$ into the formula: $a_{5}=-2\times(-84)-4=168-4=164$ .