The first two numbers in a sequence h are h(1) = 2 and h(2) = 6.

1. If h is an arithmetic sequence, write a definition for the nth term of h. Explain
or show your reasoning.


2. If h is a geometric sequence, write down a definition for the nth term of h. Show reasoning

Answers

Answer 1

Answer:

Step-by-step explanation:

Given the first two numbers of a sequence as 2, 6...

If it is an arithmetic difference, the common difference will be d = 6-2 = 4

Formula for calculating nth term of an ARITHMETIC sequence Tn = a+(n-1)d

a is the first term = 2

d is the common difference = 4

n is the number if terms

Substituting the given values in the formula.

Nth term Tn = 2+(n-1)4

Tn = 2+4n-4

Tn = 4n-4+2

Tn = 4n-2

2) If the sequence us a geometric sequence

Nth term of the sequence Tn = ar^(n-1)

r is the common ratio

r is gotten by the ratio of the terms I.e

r = T2/T1

r = 6/2

r = 3

Since a = 2

Tn = 2(3)^(n-1)

Hence the nth term of the geometric sequence is Tn = 2(3)^(n-1)


Related Questions

HELPPP PLEASE!!!
The store has 61 guppies divided into 8 aquarium tanks, and a small display aquarium on
the sales counter. Each of the 8 tanks has an even number in them with the remaining
guppies in the display aquarium. How many guppies are in each aquarium and in the
display aquarium?

Answers

Answer:

5 in display, 7 in each aquarium.

Step-by-step explanation:

18 is 2/3 of what number

Answers

18 is 2/3 of 27.

Hope this helps!

The number 18 is 2/3 of the number 27.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that 18 is 2/3 rd of the number. The value of the unknown number will be calculated as,

2 / 3 x = 18

x = ( 18 x 3 ) / 2

x = 9 x 3

x = 27

Therefore, the unknown number will be 27.

To know more about an expression follow

https://brainly.com/question/2459749

#SPJ2

Point O is between points Mand N on line segment MN. O is the midpoint of line segment MN if
ON = NM
OM = NM
ON + OM = MN
ON = OM

Answers

Diagram:
M------------O-------------N
................. ^ midpoint
Obviously if O is the *mid*point, then it is exactly halfway between M and N. That also means it has bisected the segment into two equal parts.
On one side you have MO (or OM, if you like)
On the other side you have ON.
In order for O to be the midpoint:
ON = OM

Using the statements: If it is Friday, then I will get paid. It is Friday. Write the conclusion

Answers

Umm... You will get paid

WILL MARK BRAINLIEST NEED IT ASAP

Answers

Answer:

8

Step-by-step explanation:

6 x 9=54. 54+10=64. the square root of 64 = 8

Answer:

ANSWER IS 8

Step-by-step explanation:

as a fraction:
(i) 48%
(ii) 220%
(iii) 2.5%

Answers

Answer:

48% = 48/ 100 = 12/25220% = 220/100=11/52.5% = 25/1000 = 1/40
Given Percentage:

i. 48%

ii. 220%

iii. 2.5%

To Convert:

The given percentage into fractions.

Answer:

[tex] \large \purple {\tt {i. \: 48\% = \frac{48}{100} = \frac{12}{25}}} [/tex]

[tex] \large \pink {\tt {ii. \: 220\% = \frac{220}{100} = \frac{11}{5}}} [/tex]

[tex] \large \blue {\tt {iii. \: 2.5\% = \frac{2.5}{100} = \frac{1}{40}}} [/tex]

Simplify. 4−8÷2+3
i need help with it

Answers

Answer:

3

Step-by-step explanation:

Using PEMDAS (Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction), You do 8/2 first, which equals 4, then add 3 which turns 4 into a 7, then finally subtract 4 and your final answer is 3.

Answer:

3

Step-by-step explanation:

I took the test >.<

The density of a substance can be found by dividing the mass of the substance by the volume of the substance. A sheet of pure iron has a mass of 500 grams and a volume of 4 in3. Write an equation of the form m=dv, where m represents the mass of a sheet of iron in grams, v represents the volume of a sheet of iron in cubic inches, and d is a constant, the density of iron in grams per cubic inch

Answers

Answer:

D=375g/cubic inch

Step-by-step explanation:

D=500 divided by 4/3

The price of an item has been reduced by 55%. The original price was $53. what is the price now

Answers

Answer:

$29.15

Step-by-step explanation:

Step 1:

$53 × 55%

Step 2:

53 × 0.53

Answer:

29.15

Hope This Helps :)

Which problem is the same as 4 + 5

Answers

Answer:

6+3

Step-by-step explanation:

Evaluate each expression if a = 4, b = 6, and c = 2.

Answers

Answer:

26

Step-by-step explanation:

ab+c

plug in #s

4(6)+2

start to solve

24+2

26

What two numbers multiply to 45 and add up to 14

Answers

Answer:

5 x 9 = 45 and 5+9= 14

Step-by-step explanation:

brainliest please

5 and 9 (5 x 9) = 45, and (5+9) = 14

What is 4 divided by 348?

Answers

Answer:

4/348 = 0.01149425287

348/4 = 87

Step-by-step explanation:

348 divided by 4 is 87

4 divided by 348 is 0.01149425287

Hope this helps you :)

1/4 of a number minus 8 is -23

Answers

Answer:

I have solved it u can have a look.

describe the domain and range

Answers

Answer:

see below

Step-by-step explanation:

The domain is the input values

The domain is the resistance values

D: { 4,6,48,80,120}

The range is the output values

The range is the current values

R : { .1,.15,.25,2,3)

is the inequality always sometimes or never true?
9x+2(2+x)<5+9x​

Answers

Answer:

9x+7=5x-3

Step-by-step: are u looking for this?

What are the values of a and b on the number line?

Answers

Answer:

B is the answer

Step-by-step explanation:

Use elimination to solve and match each system of equations to the correct solution . I’ll mark u brainliest

-3x+8y=73
X-7y=-46

Answers

Answer:

Step-by-step explanation:

Let's solve for x.

−3x+8y=73

Step 1: Add -8y to both sides.

−3x+8y+−8y=73+−8y

−3x=−8y+73

Step 2: Divide both sides by -3.

−3x

−3

=

−8y+73

−3

x=

8

3

y+

−73

3

Answer:

x=

8

3

y+

−73

3

x−7y=−46

Step 1: Add 7y to both sides.

x−7y+7y=−46+7y

x=7y−46

Answer:

x=7y−46

Given that f(x) = -x and g(x) = 2x - 1. Find the value of f(3) - g(-4).

Answers

Answer:

hope it will help

Step-by-step explanation:

f(3) - (-4)

-3 +8+1

6

Answer:

Step-by-step explanation:

f(3) = -4

g(-4) = 2(-4) - 1

           -8 - 1 = -9

-4 - (-9) = -4 + 9 = 5

Help!! no can seem to help me :/

Answers

Answer:

[tex]7 {}^{0} = 1[/tex].

In any number if the power of the number is 0,then it will be 1.

What is 18=3(3x-6) algebra 1

Answers

Answer:

x=4 i believe

Step-by-step explanation:

1st.      move terms

       -3x+6=-6

2nd.      calculate the difference

       -3x=-12

3rd.     divide both side to get x alone

      x= 4

-4(4x + 4) + 7(1 + 9x)

Answers

Answer:

47x - 9

Step-by-step explanation:

-4(4x + 4) + 7(1 + 9x)

-16x -16 + 7 + 63x

47x -9

You can find what x = because there is no = sign. This is in simplest form.

Answer:

47x -9

Step-by-step explanation:

[tex]-4(4x + 4) + 7(1 + 9x)\\\\\mathrm{Expand}\:-4\left(4x+4\right):\quad -16x-16\\=-16x-16+7\left(1+9x\right)\\\\\mathrm{Expand}\:7\left(1+9x\right):\quad 7+63x\\=-16x-16+7+63x\\\\\mathrm{Simplify}\:-16x-16+7+63x:\\\quad 47x-9[/tex]

jamie's string is 10ft 1in long. emma's string is 6ft 4in long. how much longer is jamie's string

Answers

Answer:

Jamie's string is 3ft and 9in

Step-by-step explanation:

10ft 1in

-6ft 4in

=3ft 9in

Answer:

3ft 9 in

Step-by-step explanation:

So, in each foot there's 12 inches. Knowing that, the operation you use is subtraction. So you do 10 ft 1 in - 6 ft 4 in. If you do that operation knowing that 12 inches=1 foot, then you should get 3 ft 9 in.

Please let me know if there is still any confusion.

solve m = 10x - x for x

Answers

Answer:

X = M/9

Step-by-step explanation:

Solve 0.5y+y/3=0.25y+7​
please answer this question

Answers

Answer:

y = 28

Step-by-step explanation:

0.5y + y/ 3 = 0.25y + 7

1.5y / 3 = 0.25y + 7

y/2 = 0.25y + 7

y = ( 0.25y + 7)*2

y = 0.5y + 14

y - 0.5y = 14

0.5y = 14

y = 14/0.5

y = 28

Mrs. Burrell is buying donuts for a morning study session. She can spent $35. If it costs $3 per donut and $2 for a chocolate milk for herself, how many donuts did she buy for her students?

Answers

Answer: 11 donuts

Step-by-step explanation:

Need a answer ASAP ! An explanation and answer please

Answers

Answer:

i wish i could help but im dumb

Step-by-step explanation:

A car travels 100 meters in 5 seconds. Whats is the speed of the car

Answers

Answer:

20m/s

Step-by-step explanation:

[tex]Speed=Distance\div Time[/tex]

[tex]Speed=100m \div 5s[/tex]

[tex]Speed = 20m/s[/tex]

Asia has $15.45 to buy chips for a party. Each bag costs $2.13. How many can she buy?

Answers

Answer:

She can buy 7 bags of chips

Step-by-step explanation:

just take 15.45 and divide it by 2.13

Answer:

7

Step-by-step explanation:

If you divide both numbers you will get 7.253. When it's a decimal, you will round down, which gives you the answer of 7

describe an infinite solution

Answers

Infinite solution is when there is exactly one solution no solution is where there isn’t an answer to the equation or it don’t make sense

Answer: The first is when we have what is called infinite solutions. This happens when all numbers are solutions. The equation 2x + 3 = x + x + 3 is an example of an equation that has an infinite number of solutions. ...

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