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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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Find trigonometric ratios using multiple identities

Full solution

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: $\newline$ $a_{4} = -4a_{3} - 4$ $\newline$ $a_{4} = -4(133) - 4$ $\newline$ $a_{4} = -532 - 4$ $\newline$ $a_{4} = -536$

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