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kolezko [41]
2 years ago
15

The first five terms of a quadratic sequence are 3, 12, 25, 42, 63.

Mathematics
1 answer:
skad [1K]2 years ago
7 0

Since we know the sequence is quadratic, we expect the n-th term to have the general form

x_n = an^2 + bn + c

Plug in the first 3 known values of the sequence to form a system of equations.

x_1 = 3 = a + b + c

x_2 = 12 = 4a + 2b + c

x_3 = 25 = 9a + 3b + c

Eliminating c gives

(4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9

(9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11

Eliminating b gives

(4a + b) - (3a + b) = 11 - 9 \implies a = 2

Solving for b,c, we get

4a + b = 11 \implies b = 11-4\cdot2 = 3

a+b+c=3 \implies c=3-2-3 = -2

So, the n-th term of the sequence is

x_n = \boxed{2n^2 + 3n - 2}

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Can someone help me with this
mash [69]

The center of the circle is (h,k) = (-2,-3)

The radius of the circle is r = 2

The standard form of equation of the circle is

{(x + 2)}^{2}  +  {(y + 3)}^{2}  = 4

<h3>How to find the center, radius and standrad form of the circle?</h3>

The general form of equation of the circle is

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

Here, (h,k) means centre of the circle.

r means radius of the circle.

given that coordinate points of centre of circle is (-2,-3).

Hence the (h,k) = (-2,-3)

<h3>How to find the radius of the circle?</h3>

Now to find the radius of the circle

The distance from a circle's centre to its circumference is its radius.

The distance from a circle's centre (-2,-3) to its circumference (0,-3) is its radius.

using the formula, distance between the two points to obtain radius.

d =  \sqrt{(x1 - x2) {}^{2}  +  {(y1 - y2)}^{2} }  \\ r =  \sqrt{ {( - 2 - 0)}^{2} +  {( - 3 - ( - 3))}^{2}  }  \\ r =  \sqrt{ {( - 2)}^{2} +  {( - 3 + 3)}^{2}  }  \\ r =  \sqrt{ {4}^{2} + 0 }  \\ r =  \sqrt{4}  \\ r = 2

<h3>How to find the standard form of equation of the circle?</h3>

(h,k) = (-2,-3)

r = 2

subtitue the (h,k) and r values to get the standard form of equation of the circle.

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

{(x - ( - 2))}^{2}  +  {(y - ( - 3))}^{2} =  {r}^{2}

{(x + 2)}^{2}  +  {(y + 3)}^{2}  = 4

Learn more about circle, refer:

brainly.com/question/24810873

#SPJ9

5 0
1 year ago
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Answer: -2.85

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5(22/20)= 110/100= 1.10

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