If a_(1)=7 and a_(n+1)=4a_(n)-4 then find the value of a_(5). Answer:

Given Sequence and Formula: We are given the first term of the sequence, a_(1) = 7, and the recursive formula a_(n+1) = 4a_(n) - 4. To find a_(5), we need to find the values of a_(2), a_(3), and a_(4) first, using the recursive formula.Find a_(2): Let's find a_(2) using the recursive formula: a_(2) = 4a_(1) - 4 a_(2) = 4(7) - 4 a_(2) = 28 - 4 a_(2) = 24Find a_(3): Now, let's find a_(3) using the recursive formula: a_(3) = 4a_(2) - 4 a_(3) = 4(24) - 4 a_(3) = 96 - 4 a_(3) = 92Find a_(4): Next, we find a_(4) using the recursive formula: a_(4) = 4a_(3) - 4 a_(4) = 4(92) - 4 a_(4) = 368 - 4 a_(4) = 364Find a_(5): Finally, we find a_(5) using the recursive formula: a_(5) = 4a_(4) - 4 a_(5) = 4(364) - 4 a_(5) = 1456 - 4 a_(5) = 1452

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If
a_(1)=7 and
a_(n+1)=4a_(n)-4 then find the value of
a_(5).
Answer:

If $a_{1}=7$ and $a_{n+1}=4 a_{n}-4$ then find the value of $a_{5}$ . $\newline$ Answer:

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Q. If

a_{1}=7

and

a_{n+1}=4 a_{n}-4

then find the value of

a_{5}

\newline

Answer:

Given Sequence and Formula: We are given the first term of the sequence, $a_{1} = 7$ , and the recursive formula $a_{n+1} = 4a_{n} - 4$ . To find $a_{5}$ , we need to find the values of $a_{2}$ , $a_{3}$ , and $a_{4}$ first, using the recursive formula.
Find $a_{2}$ : Let's find $a_{2}$ using the recursive formula: $\newline$ $a_{2} = 4a_{1} - 4$ $\newline$ $a_{2} = 4(7) - 4$ $\newline$ $a_{2} = 28 - 4$ $\newline$ $a_{2} = 24$
Find $a_{3}$ : Now, let's find $a_{3}$ using the recursive formula: $\newline$ $a_{3} = 4a_{2} - 4$ $\newline$ $a_{3} = 4(24) - 4$ $\newline$ $a_{3} = 96 - 4$ $\newline$ $a_{3} = 92$
Find $a_{4}$ : Next, we find $a_{4}$ using the recursive formula: $\newline$ $a_{4} = 4a_{3} - 4$ $\newline$ $a_{4} = 4(92) - 4$ $\newline$ $a_{4} = 368 - 4$ $\newline$ $a_{4} = 364$
Find $a_{5}$ : Finally, we find $a_{5}$ using the recursive formula: $\newline$ $a_{5} = 4a_{4} - 4$ $\newline$ $a_{5} = 4(364) - 4$ $\newline$ $a_{5} = 1456 - 4$ $\newline$ $a_{5} = 1452$