If a_(1)=10 and a_(n+1)=-3a_(n)+5 then find the value of a_(4). Answer:

Given Information: We are given the first term of the sequence, a_(1)=10, and the recursive formula a_(n+1)=-3a_(n)+5. To find a_(4), we need to find a_(2), a_(3), and then a_(4) using the recursive formula.Find a_(2): First, let's find a_(2) using the recursive formula with n=1. a_(2) = -3a_(1) + 5 a_(2) = -3(10) + 5 a_(2) = -30 + 5 a_(2) = -25Find a_(3): Next, we'll find a_(3) using the recursive formula with n=2. a_(3) = -3a_(2) + 5 a_(3) = -3(-25) + 5 a_(3) = 75 + 5 a_(3) = 80Find a_(4): Finally, we'll find a_(4) using the recursive formula with n=3. a_(4) = -3a_(3) + 5 a_(4) = -3(80) + 5 a_(4) = -240 + 5 a_(4) = -235

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If
a_(1)=10 and
a_(n+1)=-3a_(n)+5 then find the value of
a_(4).
Answer:

If $a_{1}=10$ and $a_{n+1}=-3 a_{n}+5$ then find the value of $a_{4}$ . $\newline$ Answer:

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Precalculus

Find trigonometric ratios using multiple identities

Full solution

Q. If

a_{1}=10

and

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

then find the value of

a_{4}

\newline

Answer:

Given Information: We are given the first term of the sequence, $a_{1}=10$ , and the recursive formula $a_{n+1}=-3a_{n}+5$ . To find $a_{4}$ , we need to find $a_{2}$ , $a_{3}$ , and then $a_{4}$ using the recursive formula.
Find $a_{2}$ : First, let's find $a_{2}$ using the recursive formula with $n=1$ .
$a_{2} = -3a_{1} + 5$
$a_{2} = -3(10) + 5$
$a_{2} = -30 + 5$
$a_{2} = -25$
Find $a_{3}$ : Next, we'll find $a_{3}$ using the recursive formula with $n=2$ . $\newline$ $a_{3} = -3a_{2} + 5$ $\newline$ $a_{3} = -3(-25) + 5$ $\newline$ $a_{3} = 75 + 5$ $\newline$ $a_{3} = 80$
Find $a_{4}$ : Finally, we'll find $a_{4}$ using the recursive formula with $n=3$ . $\newline$ $a_{4} = -3a_{3} + 5$ $\newline$ $a_{4} = -3(80) + 5$ $\newline$ $a_{4} = -240 + 5$ $\newline$ $a_{4} = -235$