If f(1)=7 and f(n+1)=3f(n)-5 then find the value of f(5). Answer:

Understand recursive formula: Understand the recursive formula and initial condition. The recursive formula given is f(n+1)=3f(n)-5, and we know that f(1)=7. This means that to find f(5), we need to find the values of f(2), f(3), and f(4) first, using the recursive formula.Find f(2): Find the value of f(2). Using the recursive formula, we substitute n=1 to find f(2). f(2) = 3f(1) - 5 f(2) = 3(7) - 5 f(2) = 21 - 5 f(2) = 16Find f(3): Find the value of f(3). Using the recursive formula, we substitute n=2 to find f(3). f(3) = 3f(2) - 5 f(3) = 3(16) - 5 f(3) = 48 - 5 f(3) = 43Find f(4): Find the value of f(4). Using the recursive formula, we substitute n=3 to find f(4). f(4) = 3f(3) - 5 f(4) = 3(43) - 5 f(4) = 129 - 5 f(4) = 124Find f(5): Find the value of f(5). Using the recursive formula, we substitute n=4 to find f(5). f(5) = 3f(4) - 5 f(5) = 3(124) - 5 f(5) = 372 - 5 f(5) = 367

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If
f(1)=7 and
f(n+1)=3f(n)-5 then find the value of
f(5).
Answer:

If $f(1)=7$ and $f(n+1)=3 f(n)-5$ then find the value of $f(5)$ . $\newline$ Answer:

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Math Problems

Grade 8

Write and solve direct variation equations

Full solution

Q. If

f(1)=7

and

f(n+1)=3 f(n)-5

then find the value of

f(5)

\newline

Answer:

Understand recursive formula: Understand the recursive formula and initial condition. $\newline$ The recursive formula given is $f(n+1)=3f(n)-5$ , and we know that $f(1)=7$ . This means that to find $f(5)$ , we need to find the values of $f(2)$ , $f(3)$ , and $f(4)$ first, using the recursive formula.
Find $f(2)$ : Find the value of $f(2)$ . Using the recursive formula, we substitute $n=1$ to find $f(2)$ . $f(2) = 3f(1) - 5$ $f(2) = 3(7) - 5$ $f(2) = 21 - 5$ $f(2) = 16$
Find $f(3)$ : Find the value of $f(3)$ . Using the recursive formula, we substitute $n=2$ to find $f(3)$ . $f(3) = 3f(2) - 5$ $f(3) = 3(16) - 5$ $f(3) = 48 - 5$ $f(3) = 43$
Find $f(4)$ : Find the value of $f(4)$ . Using the recursive formula, we substitute $n=3$ to find $f(4)$ . $f(4) = 3f(3) - 5$ $f(4) = 3(43) - 5$ $f(4) = 129 - 5$ $f(4) = 124$
Find $f(5)$ : Find the value of $f(5)$ . Using the recursive formula, we substitute $n=4$ to find $f(5)$ . $f(5) = 3f(4) - 5$ $f(5) = 3(124) - 5$ $f(5) = 372 - 5$ $f(5) = 367$