If a_(1)=9 and a_(n+1)=2a_(n)+2 then find the value of a_(5). Answer:

Identify Given Sequence: Identify the given sequence and the recursive formula. We are given the first term of the sequence, a_(1) = 9, and the recursive formula a_(n+1) = 2a_(n) + 2, which tells us how to find any term in the sequence based on the previous term.Find a_(2): Use the recursive formula to find a_(2). We know a_(1) = 9, so we can find a_(2) by plugging a_(1) into the recursive formula: a_(2) = 2a_(1) + 2 a_(2) = 2 * 9 + 2 a_(2) = 18 + 2 a_(2) = 20Find a_(3): Use the recursive formula to find a_(3). Now that we have a_(2), we can find a_(3): a_(3) = 2a_(2) + 2 a_(3) = 2 * 20 + 2 a_(3) = 40 + 2 a_(3) = 42Find a_(4): Use the recursive formula to find a_(4). With a_(3) found, we can find a_(4): a_(4) = 2a_(3) + 2 a_(4) = 2 * 42 + 2 a_(4) = 84 + 2 a_(4) = 86Find a_(5): Use the recursive formula to find a_(5). Finally, we use a_(4) to find a_(5): a_(5) = 2a_(4) + 2 a_(5) = 2 * 86 + 2 a_(5) = 172 + 2 a_(5) = 174

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If
a_(1)=9 and
a_(n+1)=2a_(n)+2 then find the value of
a_(5).
Answer:

If $a_{1}=9$ and $a_{n+1}=2 a_{n}+2$ then find the value of $a_{5}$ . $\newline$ Answer:

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Grade 8

Write and solve direct variation equations

Full solution

Q. If

a_{1}=9

and

a_{n+1}=2 a_{n}+2

then find the value of

a_{5}

\newline

Answer:

Identify Given Sequence: Identify the given sequence and the recursive formula. $\newline$ We are given the first term of the sequence, $a_{1} = 9$ , and the recursive formula $a_{n+1} = 2a_{n} + 2$ , which tells us how to find any term in the sequence based on the previous term.
Find $a_{2}$ : Use the recursive formula to find $a_{2}$ . We know $a_{1} = 9$ , so we can find $a_{2}$ by plugging $a_{1}$ into the recursive formula: $a_{2} = 2a_{1} + 2$ $a_{2} = 2 \times 9 + 2$ $a_{2} = 18 + 2$ $a_{2} = 20$
Find $a_{3}$ : Use the recursive formula to find $a_{3}$ . Now that we have $a_{2}$ , we can find $a_{3}$ : $a_{3} = 2a_{2} + 2$ $a_{3} = 2 \times 20 + 2$ $a_{3} = 40 + 2$ $a_{3} = 42$
Find $a_{4}$ : Use the recursive formula to find $a_{4}$ . With $a_{3}$ found, we can find $a_{4}$ : $a_{4} = 2a_{3} + 2$ $a_{4} = 2 \times 42 + 2$ $a_{4} = 84 + 2$ $a_{4} = 86$
Find $a_{5}$ : Use the recursive formula to find $a_{5}$ . Finally, we use $a_{4}$ to find $a_{5}$ : $a_{5} = 2a_{4} + 2$ $a_{5} = 2 \times 86 + 2$ $a_{5} = 172 + 2$ $a_{5} = 174$