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4 years ago

Is the sequence 5,9,15———-an arithmetic?

Mathematics

2 answers:

Mademuasel [1]4 years ago

6 0

Answer:

No, the given sequence is not arithmetic.

Step-by-step explanation:

The given sequence is

$5,9,15,....$

The first term is 5.

A sequence is an arithmetic, if the difference between any two consecutive terms are same.

The difference between terms are

$d_1=9-5=4$

$d_2=15-9=6$

$d_1\neq d_2$

Since the difference between consecutive terms are not same, therefore given sequence is not arithmetic.

Veseljchak [2.6K]4 years ago

4 0

Answer:

5, 9, 15,....is not an arithmetic sequence.

Step-by-step explanation:

Arithmetic sequence is a sequence in which difference between the consecutive terms is constant.

Example: 0 , 5, 10, 15, 20 is an arithmetic sequence with common difference of 5 between the terms.

Consider the given sequence,

5, 9, 15,....

Here, $a_1=5\\\\a_2=9\\\\a_3=15$

We first find the difference between the terms,

$a_2-a_1=9-5=4$

$a_3-a_2=15-9=6$

Since the difference is not constant .

So,it is not an arithmetic sequence.

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Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

1 year ago

(8+5i) + (10+6i)-(3+6i)

Natali [406]

Answer:

15 + 5i

Step-by-step explanation:

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3 years ago

A company that manufactures guitars has a fixed cost of $100,000. It costs $100 to produce each guitar and the selling price is

miv72 [106K]

a. Write the cost function:: C(x) = 100x + 100,000 where x is number of guitars

---------------------------------

b. Write the revenue function:: R(x) = 300x where x is number of guitars

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c. Find the profit function.

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P(x) = R(x) - C(x)

P(x) = [ R(x) ] - [ C(x) ]

P(x) = [ 300x ] - [ 100x+100,000 ]

P(x) = 300x - 100x-100,000

P(x) = 200x - 100,000

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3 years ago

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kirza4 [7]

Answer:

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Step-by-step explanation:

Area = side x side

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(2x + 1) (x+5)

^These are your two sides

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Answer:

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Step-by-step explanation:

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3 years ago