If a_(1)=9 and a_(n)=-4a_(n-1)+4 then find the value of a_(3). Answer:

Find a_(2): We are given the first term of the sequence, a_(1)=9, and the recursive formula for the sequence, a_(n)=-4a_(n-1)+4. To find a_(3), we first need to find a_(2) using the recursive formula. a_(2) = -4a_(1) + 4 Substitute the value of a_(1) into the formula. a_(2) = -4(9) + 4 Calculate the value of a_(2). a_(2) = -36 + 4 a_(2) = -32Calculate a_(3): Now that we have a_(2), we can use the recursive formula again to find a_(3). a_(3) = -4a_(2) + 4 Substitute the value of a_(2) into the formula. a_(3) = -4(-32) + 4 Calculate the value of a_(3). a_(3) = 128 + 4 a_(3) = 132

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If
a_(1)=9 and
a_(n)=-4a_(n-1)+4 then find the value of
a_(3).
Answer:

If $a_{1}=9$ and $a_{n}=-4 a_{n-1}+4$ then find the value of $a_{3}$ . $\newline$ Answer:

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Precalculus

Find trigonometric ratios using multiple identities

Full solution

Q. If

a_{1}=9

and

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

then find the value of

a_{3}

\newline

Answer:

Find $a_{2}$ : We are given the first term of the sequence, $a_{1}=9$ , and the recursive formula for the sequence, $a_{n}=-4a_{n-1}+4$ . To find $a_{3}$ , we first need to find $a_{2}$ using the recursive formula. $\newline$ $a_{2} = -4a_{1} + 4$ $\newline$ Substitute the value of $a_{1}$ into the formula. $\newline$ $a_{2} = -4(9) + 4$ $\newline$ Calculate the value of $a_{2}$ . $\newline$ $a_{2} = -36 + 4$ $\newline$ $a_{1}=9$ $0$
Calculate $a_{3}$ : Now that we have $a_{2}$ , we can use the recursive formula again to find $a_{3}$ . $\newline$ $a_{3} = -4a_{2} + 4$ $\newline$ Substitute the value of $a_{2}$ into the formula. $\newline$ $a_{3} = -4(-32) + 4$ $\newline$ Calculate the value of $a_{3}$ . $\newline$ $a_{3} = 128 + 4$ $\newline$ $a_{3} = 132$