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

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

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Find trigonometric ratios using multiple identities

Full solution

Q. If

a_{1}=9

and

a_{n+1}=4 a_{n}+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, $a_{n+1}=4a_{n}+4$ . To find $a_{3}$ , we first need to find $a_{2}$ using the recursive formula. $\newline$ Substitute $n=1$ into the recursive formula to find $a_{2}$ : $\newline$ $a_{2} = 4a_{1} + 4$ $\newline$ $a_{2} = 4(9) + 4$ $\newline$ $a_{2} = 36 + 4$ $\newline$ $a_{1}=9$ $0$
Find $a_{3}$ : Now that we have $a_{2}$ , we can use it to find $a_{3}$ by substituting $n=2$ into the recursive formula: $\newline$ $a_{3} = 4a_{2} + 4$ $\newline$ $a_{3} = 4(40) + 4$ $\newline$ $a_{3} = 160 + 4$ $\newline$ $a_{3} = 164$

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