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Cerrena [4.2K]
3 years ago
9

Find the sum of first 20 to terms of an ap in which d is equal to 7 and 20 second term is 149​

Mathematics
2 answers:
GuDViN [60]3 years ago
6 0

Answer:

1370

Step-by-step explanation:

<h3>Given</h3>
  • AP with d= 7 and a₂₂ = 149
<h3>To find</h3>
  • Sum of first 20 terms
<h3>Solution</h3>

<u>First, let's get the value of the first term:</u>

  • aₙ = a + (n-1)d
  • a₂₂ = a + 21d
  • 149 = a + 21*7
  • a = 149 - 147
  • a= 2

<u>Next, let's find the sum of the first 20 terms</u>

  • Sₙ = 1/2n(2a+ (n-1)d)
  • S₂₀ = 1/2*20(2*2 + 19*7) = 10(4 + 133) = 10*137 = 1370

<u>Answer is</u> 1370

Likurg_2 [28]3 years ago
5 0

Answer:

\frak{Given}\begin{cases} \sf{\: Common \: difference \: (d) = 7}\\\sf{ \: 22nd \ term = 149} \end{cases}

We've to find out the sum of 20 terms. So, n = 22

By using nth term Formula of the AP :

\star \ \boxed{\sf{\purple{a_{n} = a + (n -1)d}}} \\  \\ \underline{\bf{\dag} \: \mathfrak{Substituting \ Values \ in \ the \ formula \ :}}

:\implies\sf 149 = a + (22 - 1) \times 7 \\\\\\:\implies\sf 149 = a + 21 \times 7 \\\\\\:\implies\sf 149 = a + 147\\\\\\:\implies\sf a = 149 - 147\\\\\\:\implies\boxed{\frak{\purple{a = 2}}}

\therefore\underline{\textsf{ Here, we get value of the First term (a) of AP \textbf{2}}}. \\

<h2>______________________</h2>

For any Arithmetic Progression ( AP ), the sum of n terms is Given by :

\bf{\dag}\quad\large\boxed{\sf S_n = \dfrac{n}{2}\bigg \lgroup a + l\bigg \rgroup}

Where :

  • a = First Term
  • n = no. of terms
  • l = Last Term

:\implies\sf S_{22} = \dfrac{\cancel{20}}{\cancel{\:2}} \bigg(2 + 149 \bigg) \\\\\\:\implies\sf S_{22} = 10 \times 151 \\\\\\:\implies\boxed{\frak{\purple{ S_{22} = 1510}}}

\therefore\underline{\textsf{ Hence, Sum of 20 terms of the AP is \textbf{1510}}}. \\

<h3>⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀</h3>

⠀

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1) Parallel line: y=-2x-3

2) Rectangle

3) Perpendicular line: y = 0.5x + 2.5

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5) Distance: d=\sqrt{(4-3)^2+(7-1)^2}

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Step-by-step explanation:

1)

The equation of a line is in the form

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where m is the slope and q is the y-intercept.

Two lines are parallel to each other if they have same slope m.

The line given in this problem is

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So its slope is m=-2. Therefore, the only line parallel to this one is the line which have the same slope, which is:

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Since it also has m=-2

2)

We can verify that this is a rectangle by checking that the two diagonals are congruent. We have:

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- Second diagonal: d_2 = \sqrt{(1-(-5))^2+(0-2)^2}=\sqrt{6^2+(-2)^2}=6.32

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3)

Given points A (0,1) and B (-2,5), the slope of the line is:

m=\frac{5-1}{-2-0}=-2

The slope of a line perpendicular to AB is equal to the inverse reciprocal of the slope of AB, so:

m'=\frac{1}{2}

And using the slope-intercept for,

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And re-arranging,

y-1 = \frac{1}{2}x-\frac{7}{2}\\y=\frac{1}{2}x-\frac{5}{2}\\y=0.5x-2.5

4)

The endpoints of the segment are X(1,2) and Y(6,7).

We have to divide the sgment into 1/3 and 2/3 parts from X to Y, so for the x-coordinate we get:

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5)

The distance between two points A(x_A,y_A) and B(x_B,y_B) is given by

d=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}

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E(3,1)

F(4,7)

So the distance is given by

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6)

We have:

A(3,4)

B(11,3)

Point C divides the segment into two parts with 3:5 ratio.

The distance between the x-coordinates of A and B is 8 units: this means that the x-coordinate of C falls 3 units to the right of the x-coordinate of A and 5 units to the left of the x-coordinate of B, so overall, the x-coordinate of C falls at

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of the  distance between A and B.

7)

To find the perimeter, we have to calculate the length of each side:

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d_{FG}=\sqrt{(x_G-x_F)^2+(y_G-y_F)^2}=\sqrt{(-1-2)^2+(3-4)^2}=3.2

d_{GH}=\sqrt{(x_G-x_H)^2+(y_G-y_H)^2}=\sqrt{(-1-(-3))^2+(3-3)^2}=2

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So the perimeter is

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8)

The area of a triangle is

A=\frac{1}{2}(base)(height)

For this triangle,

Base = XW

Height = YZ

We calculate the length of the base and of the height:

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So the area is

A=\frac{1}{2}(XW)(YZ)=\frac{1}{2}(5.7)(2.8)=8

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A triangle is a right triangle when there is one right angle. This means that two sides of the triangle are perpendicular to each other: however, two lines are perpendicular when their slopes are opposite reciprocals. Therefore, this means that the true statement is

"Two slopes of triangle ABC are opposite reciprocals"

10)

The initial line is

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A line perpendicular to this one must have a slope which is the opposite reciprocal, so

m'=-4

Using the slope-intercept form,

y-y_0 = m'(x-x_0)

And using the point

(x_0,y_0)=(-1,5)

we find:

y-5=-4(x-(-1))

Learn more about parallel and perpendicular lines:

brainly.com/question/3414323

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