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If
f(1)=7 and
f(n)=2f(n-1)-2 then find the value of
f(3).
Answer:

If $f(1)=7$ and $f(n)=2 f(n-1)-2$ then find the value of $f(3)$ . $\newline$ Answer:

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Find trigonometric ratios using multiple identities

Full solution

Q. If

f(1)=7

and

f(n)=2 f(n-1)-2

then find the value of

f(3)

.

\newline

Answer:

Find $f(2)$ : We are given the initial condition $f(1) = 7$ and the recursive formula $f(n) = 2f(n-1) - 2$ . To find $f(3)$ , we first need to find $f(2)$ using the recursive formula. $\newline$ Using the formula, we substitute $n = 2$ to find $f(2)$ : $\newline$ $f(2) = 2f(2-1) - 2$ $\newline$ $f(2) = 2f(1) - 2$ $\newline$ $f(2) = 2 \times 7 - 2$ $\newline$ $f(1) = 7$ $0$ $\newline$ $f(1) = 7$ $1$
Find $f(3)$ : Now that we have $f(2)$ , we can use it to find $f(3)$ using the same recursive formula. $\newline$ Substitute $n = 3$ into the formula to find $f(3)$ : $\newline$ $f(3) = 2f(3-1) - 2$ $\newline$ $f(3) = 2f(2) - 2$ $\newline$ $f(3) = 2 \times 12 - 2$ $\newline$ $f(3) = 24 - 2$ $\newline$ $f(3) = 22$

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