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Ronch [10]
2 years ago
14

Identify the explicit formula for the sequence given by the following recursive formula:

Mathematics
1 answer:
Alex787 [66]2 years ago
7 0

If f(n) = f(n - 1) + 4, then

f(n - 1) = f(n - 2) + 4

and substituting this into the first equation gives

f(n) = f(n - 2) + 2•4

Similarly,

f(n - 2) = f(n - 3) + 4

so that

f(n) = f(n - 3) + 3•4

and so on.

Note the pattern:

f(n) = f(n - k) + k•4

so that when k = n - 1, we have

f(n) = f(n - (n - 1)) + (n - 1)•4

or

f(n) = f(1) + 4 (n - 1)

so that

[D] f(n) = -2 + 4 (n - 1)

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ALGEBRA 1, SEMESTER 2
SIZIF [17.4K]

So firstly, we have to find f(x) when x = 8 and x = 0. Plug the two numbers into the x variable of the function to solve for their f(x):

f(0)=\frac{2*0+3}{3*0-3}\\ f(0)=\frac{0+3}{0-3}\\ f(0)=\frac{3}{-3}\\ f(0)=-1\\ \\ f(8)=\frac{2*8+3}{3*8-3}\\ f(8)=\frac{16+3}{24-3}\\ f(8)=\frac{19}{21}

Now that we have their y's, we can use the slope, aka average rate of change, formula, which is \frac{y_2-y_1}{x_2-x_1} . Using what we have, we can solve it as such:

\frac{\frac{19}{21}-(-1)}{8-0}=\frac{\frac{40}{21}}{8}=\frac{40}{21*8}=\frac{40}{168}=\frac{5}{21}

In short, the average rate of change from x = 0 to x = 8 is 5/21.

8 0
3 years ago
Help pls so people say it’s none of these but idk I am confused.
crimeas [40]

Answer:

Volume = \pi r^2 h

2512 = 3.14 × r^2 × 8

r^2 = \displaystyle\frac{314}{3.14}

r^2 = 100

r = 10 \ cm

Diameter = 2r = 20 \ cm

Dont get confused try to understand : )

8 0
3 years ago
Read 2 more answers
HELP!!!!
ch4aika [34]

Answer:

8 y^{50}

Step-by-step explanation:

Given (64 y Superscript 100 Baseline) Superscript one-half.

Let us write it into an equation.

\left(64 y^{100}\right)^{\frac{1}{2}}

Apply radical rule: \sqrt[n]{a}=a^{\frac{1}{2}} and a^{m+n}=a^m+a^n

\begin{aligned}\left(64 y^{100}\right)^{\frac{1}{2}} &=\sqrt[2]{64 y^{100}} \\&=\sqrt[2]{8^{2} y^{50} y^{50}} \\&=\sqrt[2]{8^{2}\left(y^{50}\right)^{2}} \\&=8 y^{50}\end{aligned}

Hence, 8 y^{50} is equivalent to  (64 y Superscript 100 Baseline) Superscript one-half.

8 0
3 years ago
Can someone pls help me with this?
tiny-mole [99]
The exponent would be 3 because u have to multiply 2 three times to get 8
4 0
3 years ago
Select all the correct answers.<br> If the measure of angle 0 is 3π/4, which statements are true?
DedPeter [7]

Answer:

135 degrees

Step-by-step explanation:

8 0
2 years ago
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