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loris [4]
2 years ago
5

F(1)=-12, f(n)=2f(n-1) find first 4 terms

Mathematics
1 answer:
amid [387]2 years ago
4 0
<h3>First four terms are:   -12, -24, -48, -96</h3>

============================================

Explanation:

The notation f(1) = -12 tells us that the first term is -12.

The equation f(n) = 2*f(n-1) indicates that we're multiplying the (n-1)th term by 2 to get the nth term. Basically we multiply each term by 2 to get the next term.

-12*2 = -24

-24*2 = -48

-48*2 = -96

So the first four terms are -12, -24, -48, -96.

-----------------------------------

Alternative Approach

f(1) = -12 .... first term

f(n) = 2*f(n-1) ... nth term recursive formula

f(2) = 2*f(2-1) ... plug in n = 2

f(2) = 2*f(1)

f(2) = 2*(-12) ... plug in f(1) = -12

f(2) = -24 ... second term

f(n) = 2*f(n-1) .... resetting for the next computation

f(3) = 2*f(3-1) ... plug in n = 3

f(3) = 2*f(2)

f(3) = 2*(-24)  ... plug in f(2) = -24

f(3) = -48 .... third term

f(n) = 2*f(n-1) ... one more reset

f(4) = 2*f(4-1) .... plug in n = 4

f(4) = 2*f(3)

f(4) = 2*(-48) ... plug in f(3) = -48

f(4) = -96 ... fourth term

We get the first four terms to be -12, -24, -48, -96, which was the same as earlier.

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Solve the radical equation x – 7 = square root of -4x+28. Which statement is true about the solutions to the radical equation? T
Julli [10]

Answer:

x = 3 and 7

There are two true solutions.

Step-by-step explanation:

To solve x-7 = \sqrt{-4x+28}, use inverse operations by squaring both sides of the equal sign.

(x-7)^2 = (\sqrt{-4x+28})^2\\x^2-14x+49 = -4x+28\\x^2-14x+4x+49-28 = 0\\x^2-10x+21=0

The quadratic expression can be factored into binomials and set equal to 0 by the zero product property to find x.

(x - 3) ( x - 7) = 0

x-3 = 0 so x=3

x-7 = 0 so x=7

Now check each solution into the original equation to be sure it solve the solution and is not extraneous.

7-7 = \sqrt{-4(7)+28}\\ 0=0

and

3-7 = \sqrt{-4(3)+28}\\[tex]-4 = \sqrt{16}\\-4 =-4[/tex]

3 0
3 years ago
Write the equation of a circle with center M(2,6) and a radius of 4
ycow [4]

Answer:

(x -2)^2 + (y-6)^2 = 16

Step-by-step explanation:

The equation of a circle is of the form

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x- 2)^2 + (y-6)^2 = 4^2

(x -2)^2 + (y-6)^2 = 16

7 0
3 years ago
Solve 5x-y=5 and 2y-x^2=11 without using trial improvement
iren2701 [21]

Answer:

x = 7, y = 30  and  x = 3, y = 10

Step-by-step explanation:

5x - y = 5, then y = 5x - 5

2y - x^2 = 11

2(5x - 5) - x^2 = 11

10x - 10 - x^2 = 11

-x^2 + 10x -10 = 11

-x^2 + 10x -21 = 0

x^2 - 10x + 21 = 0

(x - 7)(x - 3) = 0

x = 7, y = 30

x = 3, y = 10

8 0
3 years ago
78 times 56 plz help me
rewona [7]
Your answer is 4,368
7 0
3 years ago
Read 2 more answers
Please help 2 questions
inna [77]

Answer:

1) 2002

2) 92

Step-by-step explanation:

1)

First, you need to find the area of the triangular base. The height of the triangle is 7, and the base is 26, meaning that the area is 7*26/2=91. Multiplying this by the length of the prism, you get 2002 cubic meters.

2)

First, you need to find the area of the trapezoidal base. The two bases of the trapezoid have lengths 12 and 11, while the height is 8, meaning that the area is 8*(12+11)/2=92 cubic centimeters.

Hope this helps!

8 0
3 years ago
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