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MrMuchimi
3 years ago
9

If a_1=4a 1 ​ =4 and a_n=(a_{n-1})^2+5a n ​ =(a n−1 ​ ) 2 +5 then find the value of a_3a 3 ​ .

Mathematics
1 answer:
Arturiano [62]3 years ago
5 0

The value of a3 for the given recursive pattern is 446

<h3>Sequence</h3>

A sequence can either follow an arithmetic progression or geometric progression or none

<h3>The terms</h3>

The given parameters are:

a_1 = 4

a_n = (a_{n-1})^2 + 5

Start by calculating a2

a_2 = (a_{2-1})^2 + 5

a_2 = (a_1)^2 + 5

Substitute 4 for a1

a_2 = 4^2 + 5

a_2 = 21

Next, calculate a3

a_3 = (a_{3-1})^2 + 5

a_3 = (a_{2})^2 + 5

Substitute 21 for a2

a_3 = 21^2 + 5

a_3 = 446

Hence, the value of a3 is 446

Read more about sequence and patterns at:

brainly.com/question/15590116

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Write the number in 2 equivalent forms as a​ fraction, decimal, or percent.0.40
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5 0
3 years ago
The diameter of a circle has length 12. The center is at*(-5, 2). Give the equation
labwork [276]

Answer:

Equation of the circle is : x^{2} + 10x + y^{2} -4y -7 =0

Step-by-step explanation:

Let us consider the image attached in the answer area.

The center<em> O</em> has the co-ordinates i.e. <em>(-5,2)</em> and the diameter given is <em>12 units</em>.

We know that radius is half of diameter.

\text{Radius = }\dfrac{\text{Diameter}}{2}

\text{Radius = }\dfrac{12}{2}\\\Rightarrow \text{Radius = 6units}

The equation for circle given the center and radius, can be represented as:

(x-a)^{2}+ (y-b)^{2} = r^{2}

Where <em>(a,b)</em> is the co-ordinate of center and <em>r</em> is the radius.

Let us consider the following formula:

(p+q)^2 = p^{2}+ q^{2} +2pq\\(p-q)^2 = p^{2}+ q^{2} -2pq

(x-(-5))^{2}+ (y-2)^{2} = 6^{2}\\\Rightarrow (x+5)^{2}+ (y-2)^{2} = 36\\\Rightarrow x^{2} + 25 + 10x +y^{2} + 4-4y=36\\\Rightarrow x^{2} + 10x +y^{2} -4y-7=0

Hence, Equation of the circle is : x^{2} + 10x + y^{2} -4y -7 =0

4 0
3 years ago
If f(x) = 3x2 1 and g(x) = 1 – x, what is the value of (f –
pychu [463]
F(x) = 3x^2 + 1
g(x) = 1 - x
(f - g)(x) = 3x^2 + 1 - (1 - x) = 3x^2 + 1 - 1 + x = 3x^2 + x
(f - g)(2) = 3(2)^2 + 2 = 3(4) + 2 = 12 + 2 = 14.
4 0
3 years ago
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