(1.3) Sequence A: 4; 7; 10; 13; 16; Sequence B: 5; 10; 20; 40; 80; .......... Sequence C: 2; 5; 10; 17; 26; (1.3.1) Write down the next three numbers in each of given sequences. (3) Sequence A Sequence B: Sequence C: (1.3.2) Write down how you decided what the next number would be in each of the three sequences. (3) Sequence A: Sequence B: Sequence C ​

Answers

Answer 1

Answer with Step-by -step explanation:

Sequence A;4,7,10,13,16

[tex]a_2-a_1=7-4=3[/tex]

[tex]a_3-a_2=10-7=3[/tex]

The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.

Common difference, d=3

a=4

[tex]a_n=a+(n-1)d[/tex]

[tex]a_6=a+5d=4+5\times 3=19[/tex]

[tex]a_7=a+6d=4+6(3)=22[/tex]

[tex]a_8=a+7d=4+7(3)=25[/tex]

Sequence B: 5,10,20,40,80,...

[tex]a_1=5,a_2=10,a_3=20[/tex]

[tex]\frac{a_2}{a_1}=\frac{10}{2}=2[/tex]

[tex]\frac{a_3}{a_2}=\frac{20}{10}=2[/tex]

The ratio  of two consecutive terms is equal. Therefore, it forms geometric sequence.

Common ratio, r=2

a=5

[tex]a_n=a r^{n-1}[/tex]

[tex]a_6=ar^5=5(2)^5=160[/tex]

[tex]a_7=ar^6=5(2^6)=320[/tex]

[tex]a_8=ar^7=5(2^7)=640[/tex]

Sequence C:2,5,10,17,26,..

a1=2

[tex]a_2=5=2+3=a_1+3[/tex]

[tex]a_3=10=5+5=a_2+5[/tex]

[tex]a_4=17=10+7=a_3+7[/tex]

[tex]a_5=26=17+9=a_4+9[/tex]

From the following pattern

We can get

[tex]a_6=a_5+11=26+11=37[/tex]

[tex]a_7=a_6+13=37+13=50[/tex]

[tex]a_8=a_7+15=50+15=65[/tex]


Related Questions

Please help ASAP!!!
A rectangle is formed by placing two identical squares side by side. the area of the rectangle is 892 cm2. What is the perimeter of the square?

Answers

Answer:

288 cm^2

Step-by-step explanation:

If you have 2 congruent squares, side by side, the perimeter is 6*sidelength.

We divide 72 by 6 to find sidelength, and get 12.

We square 12 to find the area of a square, and get 144.

Multiply by 2 to find the area of the rectangle, and get 288 cm^2

A light bulb consumes 3600 watt-hours per day. How many watt-hours does it consume in 4 days and 18 hours?

Answers

Answer:

17,100

Step-by-step explanation:

A light bulb consumes 3600 watts per day

Therefore the number of watts consumed in 4 days 18 hours can be calculated as follows

3600= 24 hours

x= 1 hour

= 3600/24

= 150 watts in an hour

3600×4

= 14,400

150×18

= 2,700

Total watts

= 14,400+2700

= 17,100

Hence the number if watss produced in 4 days 18 hours is 17,100 watts

What the hcf of 24 and 180

Answers

Answer:

12

Step-by-step explanation:

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180


What percent of all students are middle schools

Answers

125/300 x 100 = 41.6666% (or round up to 42%)

42% of all students are in middle school.

3
JK, KL, and IJ are all tangent to o (not drawn to scale). JA = 8, AL = 11, and
CK = 10. Find the perimeter of AJKL.

Answers

Answer:

[tex]P = 58[/tex]

Step-by-step explanation:

The image if the circle and triangle can be found online

Given

[tex]JA = 8[/tex]

[tex]AL = 8[/tex]

[tex]CK = 10[/tex]

Required

The perimeter of JKL

Since the mid-points of the tangents are A, B and C respectively.

[tex]JK = JB + BK[/tex]

Where

[tex]JB = JA = 8[/tex]

[tex]BK = CK = 10[/tex]

So:

[tex]JK =8+10 =18[/tex]

[tex]JL = JA + AL[/tex]

[tex]JL = 8+11 = 19[/tex]

[tex]KL = CL + CK[/tex]

Where

[tex]CL =AL = 11[/tex]

So:

[tex]KL = 11+10 = 21[/tex]

So, the perimeter (P) is:

[tex]P = JK+ KL +JL[/tex]

[tex]P = 18 + 19 + 21[/tex]

[tex]P = 58[/tex]

If a line has a slope of 3, what is the slope of a line perpendicular to it?

Answers

Answer:

- [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex]

Here m = 3 , then

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{3}[/tex]

What is the measure of _X in degrees?
O A. Cannot be determined
O B. 20°
O C. 40°
O D. 70°

Answers

Your answer would be C / 40
Answer: C. 40°


Step 1: Determine the type of triangle

The shape in the picture is an isosceles triangle. This is determined because two sides share the same length. This will mean that two angles will also share the same measurement, helping us to find our answer.

Step 2: Write an equation

Now that we have identified the type of triangle, we can write an equation to solve. Two angles will be equal to 70, so subtract 70 twice from 180. It will be taken away from 180, since in a triangle the three angles are equal to 180 degrees. Now we can write the equation!

X= 180-70-70

Step 3: Solve for ∠x

The final step will be to solve using the equation we have created before.

X= 180-70-70
X= 110-70
X= 40

There is the final answer. Hope this helps! Comment below for more questions.

graph:y-10=-2(x-10)grgrgrgrggrgrgrgrgrgrrgrrggr

Answers

what does the grgrgrgrgrgrgrggrgr stand for?

Answer: 14

Step-by-step explanation:

y -1 0 = -6

Ans -2 (x-10) = 14

Hope I could help :)

what is the scale factor from figure a to figure b

Answers

Scale factor from figure a to figure b = DIVIDE BY 3

{Check:- 33/3 = 11 & 15/3 = 5}

hope this helps :)

Answer:

1/3

Step-by-step explanation:

These two quadrilaterals are similar because figure A's sides are 3 times figure B's sides. Figure A's bottom is 15, while figure B's bottom is 5. To get from 15 to 5, we multiply by 1/3. This is the scale factor. All the other sides of figure A are also 3 times bigger than figure B's.

The inequality – x2 - 6 <0 has

Answers

Answer:

X es igual a 3

Step-by-step explanation:

x2 - 6 = 0

(3)2 - 6 = 0

-3x+20+7x=80 what is x? and how do I get it?

Answers

Answer:

x = 15

Step-by-step explanation:

-3x+20+7x=80

Combine like terms

4x+20 = 80

Subtract 20 from each side

4x+20 -20 = 80-20

4x = 60

Divide by 4

4x/4 = 60/4

x = 15

Which of the following is true about similar right triangles ?
A. Corresponding angles are not equal.
B. Corresponding trigger number trigonometric ratios are in proportion
C.Corresponding trigonometric ratios are equal
D.Corresponding sides are equal

Answers

Answer:

b

Step-by-step explanation:

because its alternation

The option (C) Corresponding trigonometric ratios are equal is correct.

What is the similarity law for triangles?

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

We have a statement:

Which of the following is true about similar right triangles?

As we know from the definition the two triangles have the same shape, but it is not compulsory to have the same size.

The ratio of the corresponding sides is in the same proportions

The corresponding trigonometric ratios are equal.

Thus, the option (C) Corresponding trigonometric ratios are equal is correct.

Learn more about the similarity of triangles here:

brainly.com/question/8045819

#SPJ2

Graph the image of AUVW after a translation 11 units left and 3 units down.

Answers

The units are 6,2 and 2,10

can someone help me in this problem

Answers

Answer:

8a³b

Step-by-step explanation:

I think it’s 8a³b… for the GCF

What is the length of Line segment B C?

Answers

It’d be helpful if you included an image or more information

change from improper fraction to mix number 51/7​

Answers

Answer:

7 3/7

Step-by-step explanation:

help plzzzzzzzzzzzzzzzzzzzzz

Answers

I believe it’s B but I could be wrong

the pythagorean theorem equation

Answers

A^2+b^2=c^2
Is the Pythagorean theorem

Answer:

(Altitude)^2+(Base)^2=(Hypotenuse)^2

If you input 3 into the equation below, what is the resulting y-value?
y=9

Answers

Answer:

It will still be 9.  y=9 is a horizontal line.  No matter the x value, the answer will be the same.

Step-by-step explanation:

Which equation shows the distributive property? (a) 6 x 3 + 6 x 8 = 6 x (3 + 8) (b) 5 + (22 + 19) = (5 + 22) + 19 (c) 20 x 10 = 10 x 20 (d) 45 + 7 = 7 + 45
help me please ​

Answers

The correct answer is A
the answer is A) 6x3+6x8=6(3+8)

Last question, so please help me out ASAP!

Answers

Answer:

5/18

Step-by-step explanation:

conditional probability formula:

A|B (a given b)  = (A∩B)/(B)

so

Moderate|college (moderate given college)= (moderate∩college)/college

moderate∩college= 15

college= 11+15+28= 54

15/54= 5/18

help pls i need this asap​

Answers

Answer:

I got 45 degrees

Step-by-step explanation:

knowing that where T is is 90 degrees and a triangle always= 180 degrees I just split 90 in half and got 45. I could be wrong but I hope this helps :)

A credit card has a nominal annual interest rate of 18%, and interest is compounded monthly. The cardholder uses the card to make a $30 purchase.

Which expression represents the balance on the card after 5 years, in dollars, assuming no further charges or payments are made?

Answers

Answer:

30 [tex](1 + \frac{.18}{12})^{5*12}[/tex]

Step-by-step explanation:

A wooden frame is to be constructed in the form of an isosceles trapezoid, with diagonals acting as braces to strengthen the frame. The sides of the frame each measure 5.3 feet, and the longer base measure 12.7 feet. If the angles between the sides and the longer base each measure 68.4 degrees, find the length of one brace to the nearest tenth of a foot.

Answers

Answer:

11.8 ft

Step-by-step explanation:

Since the length of one side, l = 5.3 ft, the longer base b = 12.7 ft and the one brace, d form a triangle with angle between the longer base and side being the angle facing the brace is θ = 68.4°, we use the cosine rule to find the length of thee brace.

So d² = l² + b² -2lbcosθ

So, substituting the values of the variables into the equation, we have

d² = (5.3 ft)² + (12.7 ft)² -2(5.3)(12.7)cos68.4°

d² = 28.09 ft² + 161.29 ft² - 134.62(0.3681)

d² = 189.38 ft² - 49.56 ft²

d² = 139.82 ft²

taking square-root of both sides, we have

d = √139.82 ft²

d = 11.82 ft

d ≅ 11.8 ft to the nearest tenth of a foot.

Solve 3x + 8 = 2x + 21

Answers

Answer:

x = 13 Step-by-step explanation:

3x+8=2x+21solve for x3x8-2x+21x8=21x=21-8=13solution is x=13/

HOPE IT HELPS!!!

PLZ I NEED BRAINLIEST!!

The answer is x equals to 13

1 Select the correct answer. Kalid simplified a polynomial expression as shown. (6x3 + 8x2 − 7x) − (2x2 + 3)(x − 8) step 1 (6x3 + 8x2 − 7x) − (2x3 − 16x2 + 3x − 24) step 2 6x3 + 8x2 − 7x − 2x3 − 16x2 + 3x − 24 step 3

Answers

Answer:

So, the step1 is correct.

Step-by-step explanation:

The expression is

[tex](6 x^3 + 8 x^2 - 7 x)-(2x^2 + 3)(x- 8)\\\\(6 x^3 + 8 x^2 - 7 x) - (2x^3 - 16 x^2 + 3 x - 24)\\\\6 x^3 + 8 x^2 - 7 x - 2 x^3 - 16 x^2 + 3 x - 24\\\\4 x^3 - 8 x^2 - 4 x - 24[/tex]

So, the step 1 is correct.

What are reciprocals?

Answers

Answer:

In mathematics,reciprocal is an expression or function so related to another that their product is unity; the quantity obtained by dividing the number one by a given quantity.

Answer:Rh

Step-by-step explanation:mama

randy is a car salesman who earns a base pay of $39,800 and is a paid commission of 18% for each car he sells. if x represents total sales in dollars, which equation best represents randys total pay in dollars

Answers

Answer:

39,800+x0.18= his total pay

Your Welcome

Biffy Out!!!

Jeremy uses 2 feet 3 inches of board for each birdhouse he builds. How many inches of board does he need to make 6 birdhouses?

Answers

Answer:

134inches

Step-by-step explanation:

Convert 2feet to inches

1foot= 12 inches

2feet= 12x2inches

=24inches

24inches is to 1 birdhouse

24inches x 6 equals six birdhouses

134inches

Answer:

He will need 162 inches

Step-by-step explanation:

6×2ft is 12 feet. Convert ft into inches for every 1 foot you have 12 inches. A total of 144in. Now multiply 6×3in which equals 18in. Add 144+18=162

what is the perimeter of semicircle with radius of 3cm

Answers

Answer:

198/7

Step-by-step explanation:

perimeter of semi circle= (pi) x r + d

                                     = 22/7 x 3 + 6

                                     = 198 cm

Answer:

15.42 cm

Step-by-step explanation:

perimeter of semicircle = πr + 2r

=3.14*3  + 2*3

=9.42 + 6

=15.42

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