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Nimfa-mama [501]
3 years ago
10

Write the first four terms of the sequence. rule start at 5 1/2, add 1 1/5

Mathematics
1 answer:
Hitman42 [59]3 years ago
7 0

Answer:

5\frac{1}{2},6\frac{7}{10},7\frac{9}{10},9\frac{1}{10}

Step-by-step explanation:

The first term of the sequence is

a_1=5\frac{1}{2}

To find the second term add 1\frac{1}{5} to the first term;

a_2=5\frac{1}{2}+1\frac{1}{5}=6\frac{7}{10}

To find the third term add 1\frac{1}{5} to the second term;

a_3=6\frac{7}{10}+1\frac{1}{5}=7\frac{9}{10}

To find the fourth term add 1\frac{1}{5} to the third term;

a_4=7\frac{9}{10}+1\frac{1}{5}=9\frac{1}{10}

The first four terms are

5\frac{1}{2},6\frac{7}{10},7\frac{9}{10},9\frac{1}{10}

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<h3>Given information-</h3>

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is 16 \sqrt{3} units.

As all the sides are equal thus the \Delta MNO is a equilateral triangle in which the height of the divides the triangle into two equal part of the length 8\sqrt{3} at point <em>R.</em>

<h3>Height of the triangle-</h3>

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the  \Delta MRN, the length of the hypotenuse is 16 \sqrt{3} units and the length of the base is 8\sqrt{3} units. Let <em>h </em>is the height of the triangle thus by the Pythagoras theorem,

(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2

Solve for <em>h,</em>

<em />

<em />\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end<em />

<em />

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

brainly.com/question/4268382

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Read 2 more answers
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