All categories

3 years ago

Find the 20th term of the following sequence. -6, -4, -2, 0, ... 32 44 46

Mathematics

2 answers:

Ksju [112]3 years ago

6 0

Answer:

20th term should be 32.

Step-by-step explanation:

The given sequence is -6, -4, -2, 0,.......32, 44, 46

In this sequence we can say that there is a common difference = -4 + 6 = 2 = (T₂ - T₁)

Therefore, the sequence is an arithmetic sequence.

Now explicit formula of an arithmetic sequence is given by

$T_{n}$ = a+ ( x - 1 ) d

Here a = first term

n = number of term

d = common difference

For the 20th term of the sequence.

$T_{20}$ = -6 + ( 20 - 1 ) 2

= -6 + 19 × 2

= 38 - 6

= 32

Therefore, 20th term should be 32.

mars1129 [50]3 years ago

5 0

You are adding 2 each time.

4 terms are given to you, with 5th term being 2

20 - 5 = 15

Multiply 15 with 2

15 x 2 = 30

Add the number gotten with the last number given

30 + 2 = 32

32, or (A) is your answer

hope this helps

You might be interested in

Write "100 decreased by a number k" as an algebraic expression.

shtirl [24]

Answer: 2 or B hope this helped!

5 0

2 years ago

Read 2 more answers

For the following right triangle, find the side length x. Round your answer to the nearest hundredth.

Aleksandr-060686 [28]

Answer:

$\sqrt{113}$ = x

Step-by-step explanation:

In right triangles the sum of square length of two legs is equal to square length of hypotenuse:

7^2 + 8^2 = x^2

49 + 64 = x^2 add like terms

113 = x^2 find the root for both sides

$\sqrt{113}$ = x

8 0

2 years ago

An amusement park has discovered that the brace that provides stability to the ferris

antiseptic1488 [7]

Answer:

Hence the correct answer is option (A) 4.708.

Step-by-step explanation:

Solution:-

Now, we need to find the angle of the sector by using sector formula,

$A = 28.25 ft^{2} \\r = 12ft.\\\\28.25 = \frac{\theta}{360^{o} } \times \pi \times 12^{2} \\\\\theta=\frac{28.25\times 360}{12 \times12 \times \pi} \\\\\theta =( \frac{70.625}{\\pi} )^{o}$

We now convert the angle to radian

$\theta = \frac{70.625}{\pi} \times \frac{\pi}{180}\\\\\theta = 0.39236 radian$

Now we calculate the length of arc by arc formula

$\theta=\frac{I}{12} \\\\0.39236 =\frac{I}{12}\\\\I = 4.708 feet.$

So, The length of steel that must be replaced is 4.708 ft.

4 0

3 years ago

Simplify cos^2 A/1+sin A

Stels [109]

Answer:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)$

Step-by-step explanation:

We want to simplify:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}$

Recall the Pythagorean Identity:

$\sin^2(A)+\cos^2(A)=1$

So:

$\cos^2(A)=1-\sin^2(A)$

Substitute:

$\displaystyle =\frac{1-\sin^2(A)}{1+\sin(A)}$

Factor. We can use the difference of two squares pattern:

$\displaystyle =\frac{\left(1-\sin(A))(1+\sin(A))}{1+\sin(A)}$

Cancel. Hence:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)$

7 0

2 years ago

What is the minimum number of pieces of information you think you would need in order to prove that a given quadrilateral is a s

pashok25 [27]

Answer:

At least 4 numbers of information is needed

The four are highlighted below in the explanation section

Step-by-step explanation:

1. Given that the shape has four right angles and that all its sides are congruent then it's a quadrilateral

2. If two sides are consecutively congruent it is a quadrilateral shape

3. If a rhombus contains a right angle, then it’s a square shaped rhombus

4. If a quadrilateral is both a rectangle and a rhombus, then it’s a square

3 0

3 years ago