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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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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 $n=3$ . $\newline$ $a_{4} = -3a_{3} + 5$ $\newline$ $a_{4} = -3(80) + 5$ $\newline$ $a_{4} = -240 + 5$ $\newline$ $a_{4} = -235$

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