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3 years ago

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

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 :

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

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

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

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

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

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

⠀

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

2) Rectangle

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4) x-coordinate: 2.7

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Step-by-step explanation:

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 $m=-2$

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

The diagonals are congruent, so this is a rectangle.

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

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And re-arranging,

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

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F(4,7)

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B(11,3)

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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.

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

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

$d_{EH}=\sqrt{(x_E-x_H)^2+(y_E-y_H)^2}=\sqrt{(-1-(-3))^2+(6-3)^2}=3.6$

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For this triangle,

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

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$Height =YZ=\sqrt{(x_Y-x_Z)^2+(y_Y-y_Z)^2}=\sqrt{(7-5)^2+(0-2)^2}=2.8$

So the area is

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

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"Two slopes of triangle ABC are opposite reciprocals"

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

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