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Shtirlitz [24]
3 years ago
8

Enter a recursive rule for the geometric sequence. 10, −80, 640, −5120, ... a(1)= a(n)=

Mathematics
2 answers:
Liula [17]3 years ago
6 0
The recursive formula would be:
a_1=10
\\a_{n}=a_{n-1} \times (-8)

This is because the first term, a₁, is 10.  A recursive rule is dependent upon the term before it (a(n-1)) and the common ratio.  The common ratio, or the number that each term is multiplied by, is -8.
erik [133]3 years ago
3 0

Answer:

The value is:

a(1)=10   and   a(n)=(-8)×a(n-1)

Step-by-step explanation:

We are given a sequence as:

10, -80 , 640 , -5120 ,.........

since by looking at the sequence we could see that it is a geometric progression (G.P.) with common ratio -8.

Also a(1) denotes the first term of the sequence and a(n) denotes the nth term of the sequence.

a(1)=10

Also a(n)=(-8)×a(n-1)

since a(1)=10

a(2)=(-8)×10=-80

a(3)=(-8)×(-80)=640

a(4)=(-8)×640=-5120

and so on.

Hence the answer is:

a(1)=10   and   a(n)=(-8)×a(n-1)

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Klio2033 [76]

Answer:

x = 4 - 1 = 3

Step-by-step explanation:

2(4 - y) + 3y = 9

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3 0
3 years ago
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Lostsunrise [7]

Answer:

x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}

Step-by-step explanation:

<u>Given functions</u>:

  p(x)=2x-4

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Solve for p(x) = r(x):

\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

<u>Quadratic Formula</u>

x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0

Therefore:

a=18, \quad b=-40, \quad c=-3

Substitute the values of a, b and c into the <u>quadratic formula</u> and solve for x:

\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}

Therefore, the solutions are:

x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

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2 years ago
What is the surface area of a triangular pyramid if each face has an area of 30 mm2?
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