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9 months ago

Find the 75th term of the following6, 10, 14, 18,

Mathematics

1 answer:

enot [183]9 months ago

7 0

Given the sequence:

6, 10, 14, 18,...

We will find the 75th term

The given sequence is an arithmetic sequence

Because there is a constant common differnce

d = 18 - 14 = 14 - 10 = 10 - 6 = 4

The first term = a = 6

The general formula of the arithmetic sequence is as follows:

$a_n=a+d(n-1)$

Where: n is the nth term

To find the 75th term, substitute with n = 75 and a = 6, d = 4

$a_{75}=6+4\cdot(75-1)=302$

So, the answer will be the 75th term = 302

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Step-by-step explanation:

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3 years ago

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2 years ago

A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40°W and reaches point Finally, it turns

uysha [10]

Answer:

B.18. 44 miles

Step-by-step explanation:

We are given that

Distance between A and B=8 miles

Angle B=Angle BCQ=40 degree (Alternate interior angles)

Angle ACB=180-Angle ACP-Angle BCQ

Angle ACB=180-40-40=100 degree

In triangle ABC

Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property

Substitute the values

$\angle A+40+100=180$

$\angle A+140=180$

$\angle A=180-140$

$\angle A=40$ degree

Angle A=Angle B

When two angles are equal of a triangle then the triangle is isosceles triangle.

Therefore, triangle ABC is an isosceles triangle.

$\implies BC=AC$

Now, Sine law

$\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}$

Using the sine law

$\frac{BC}{sin 40}=\frac{AB}{sin 100}$

$\frac{BC}{sin 40}=\frac{8}{sin 100}$

$BC=\frac{8\times sin40}{sin 100}$

BC=5.22

AC=BC=5.22 miles

Now, total distance covered by the boat=AB+BC+AC

Total distance covered by the boat=8+5.22+5.22=18.44 miles

Hence, option B is correct.

4 0

3 years ago