If a_(1)=8 and a_(n)=-4a_(n-1)-n then find the value of a_(4). Answer:

Given Information: We are given the first term of the sequence, a_(1)=8, and the recursive formula for the sequence, a_(n)=-4a_(n-1)-n. To find a_(4), we need to find the values of a_(2) and a_(3) first.Find a_(2): Let's find a_(2) using the recursive formula: a_(2) = -4a_(1) - 2 a_(2) = -4(8) - 2 a_(2) = -32 - 2 a_(2) = -34Find a_(3): Now, let's find a_(3) using the recursive formula: a_(3) = -4a_(2) - 3 a_(3) = -4(-34) - 3 a_(3) = 136 - 3 a_(3) = 133Find a_(4): Finally, we can find a_(4) using the recursive formula: a_(4) = -4a_(3) - 4 a_(4) = -4(133) - 4 a_(4) = -532 - 4 a_(4) = -536

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If
a_(1)=8 and
a_(n)=-4a_(n-1)-n then find the value of
a_(4).
Answer:

If $a_{1}=8$ and $a_{n}=-4 a_{n-1}-n$ then find the value of $a_{4}$ . $\newline$ Answer:

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Precalculus

Find trigonometric ratios using multiple identities

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Q. If

a_{1}=8

and

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

then find the value of

a_{4}

\newline

Answer:

Given Information: We are given the first term of the sequence, $a_{1}=8$ , and the recursive formula for the sequence, $a_{n}=-4a_{n-1}-n$ . To find $a_{4}$ , we need to find the values of $a_{2}$ and $a_{3}$ first.
Find $a_{2}$ : Let's find $a_{2}$ using the recursive formula: $\newline$ $a_{2} = -4a_{1} - 2$ $\newline$ $a_{2} = -4(8) - 2$ $\newline$ $a_{2} = -32 - 2$ $\newline$ $a_{2} = -34$
Find $a_{3}$ : Now, let's find $a_{3}$ using the recursive formula: $\newline$ $a_{3} = -4a_{2} - 3$ $\newline$ $a_{3} = -4(-34) - 3$ $\newline$ $a_{3} = 136 - 3$ $\newline$ $a_{3} = 133$
Find $a_{4}$ : Finally, we can find $a_{4}$ using the recursive formula: $\newline$ $a_{4} = -4a_{3} - 4$ $\newline$ $a_{4} = -4(133) - 4$ $\newline$ $a_{4} = -532 - 4$ $\newline$ $a_{4} = -536$