Find the recursive rule, explicit rule, and f(20)

Find The Recursive Rule, Explicit Rule, And F(20)

Answers

Answer 1

Answer:

Recursive:

[tex]f(1)=35, f(n)=f(n-1)+10[/tex]

Explicit:

[tex]f(n)=35+10(n-1)[/tex]

And the 20th term is 225.

Step-by-step explanation:

We have the sequence:

35, 45, 55, 65.

Notice that each subsequent term is 10 more than the previous term.

Therefore, our common difference is (+)10.

Recursive Rule:

The standard format for the recursive rule is:

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

Where a is the initial term and d is the common difference.

From our sequence, we know that a the initial term is 35.

And as determined, our common difference d is 10.

Substitute. Hence, our recursive rule is:

[tex]f(1)=35, f(n)=f(n-1)+10[/tex]

Explicit Rule:

The standard format for the explicit rule is:

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

Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:

[tex]f(n)=35+10(n-1)[/tex]

Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:

[tex]f(20)=35+10(20-1)[/tex]

Evaluate:

[tex]\begin{aligned} f(20)&=35+10(19) \\ f(20)&=35+190 \\ f(20)&=225 \end{aligned}[/tex]

Hence, the 20th term is 225.


Related Questions

Can anybody help plzz?? 65 points

Answers

Answer:

[tex]\frac{dy}{dx} =\frac{-8}{x^2} +2[/tex]

[tex]\frac{d^2y}{dx^2} =\frac{16}{x^3}[/tex]

Stationary Points: See below.

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Calculus

Derivative Notation dy/dx

Derivative of a Constant equals 0.

Stationary Points are where the derivative is equal to 0.

1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undef

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Quotient Rule: [tex]\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

Step 1: Define

[tex]f(x)=\frac{8}{x} +2x[/tex]

Step 2: Find 1st Derivative (dy/dx)

Quotient Rule [Basic Power]:                    [tex]f'(x)=\frac{0(x)-1(8)}{x^2} +2x[/tex]Simplify:                                                      [tex]f'(x)=\frac{-8}{x^2} +2x[/tex]Basic Power Rule:                                     [tex]f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}[/tex]Simplify:                                                     [tex]f'(x)=\frac{-8}{x^2} +2[/tex]

Step 3: 1st Derivative Test

Set 1st Derivative equal to 0:                    [tex]0=\frac{-8}{x^2} +2[/tex]Subtract 2 on both sides:                         [tex]-2=\frac{-8}{x^2}[/tex]Multiply x² on both sides:                         [tex]-2x^2=-8[/tex]Divide -2 on both sides:                           [tex]x^2=4[/tex]Square root both sides:                            [tex]x= \pm 2[/tex]

Our Critical Points (stationary points for rel max/min) are -2 and 2.

Step 4: Find 2nd Derivative (d²y/dx²)

Define:                                                      [tex]f'(x)=\frac{-8}{x^2} +2[/tex]Quotient Rule [Basic Power]:                  [tex]f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2[/tex]Simplify:                                                    [tex]f''(x)=\frac{16}{x^3} +2[/tex]Basic Power Rule:                                    [tex]f''(x)=\frac{16}{x^3}[/tex]

Step 5: 2nd Derivative Test

Set 2nd Derivative equal to 0:                    [tex]0=\frac{16}{x^3}[/tex]Solve for x:                                                    [tex]x = 0[/tex]

Our Possible Point of Inflection (stationary points for concavity) is 0.

Step 6: Find coordinates

Plug in the C.N and P.P.I into f(x) to find coordinate points.

x = -2

Substitute:                    [tex]f(-2)=\frac{8}{-2} +2(-2)[/tex]Divide/Multiply:            [tex]f(-2)=-4-4[/tex]Subtract:                       [tex]f(-2)=-8[/tex]

x = 2

Substitute:                    [tex]f(2)=\frac{8}{2} +2(2)[/tex]Divide/Multiply:            [tex]f(2)=4 +4[/tex]Add:                              [tex]f(2)=8[/tex]

x = 0

Substitute:                    [tex]f(0)=\frac{8}{0} +2(0)[/tex]Evaluate:                      [tex]f(0)=\text{unde} \text{fined}[/tex]

Step 7: Identify Behavior

See Attachment.

Point (-2, -8) is a relative max because f'(x) changes signs from + to -.

Point (2, 8) is a relative min because f'(x) changes signs from - to +.

When x = 0, there is a concavity change because f"(x) changes signs from - to +.

If 5 men paint a wall in 3hours,
How many men will paint the same wall in 3/4 hours,
working at the same rate
a)5
b)10
c)15
d)20
e)24​

Answers

Answer:20 men

Step-by-step explanation:

Answer d)20 men will paint the same wall in 3/4 hours

Help ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

There you !!!!! I hope this helped

Steve has 8 biscuits in a tin. There are 5 digestive and 3 chocolate biscuits. Steve takes two biscuits at random from the tin. Work out the probability that he chooses two different types of biscuits.

Answers

Probability that he chooses two different types of biscuits is 53.65 %.

What is probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it.

Given

Total biscuits, n = 8

Digestive biscuits = 5

Chocolate biscuits = 3

There are two patterns to chose two different biscuits; a digestive then a chocolate or a chocolate and then a digestive.

∴ The probability of choosing a digestive then a chocolate

= [tex]\frac{5}{8}\times\frac{3}{7}[/tex]

= [tex]\frac{15}{56}[/tex]

= 0.267

The probability of choosing chocolate and then a digestive.

= [tex]\frac{3}{8} \times\frac{5}{7}[/tex]

= [tex]\frac{15}{56}[/tex]

= 0.267

Hence, The combined probability

= [tex]\frac{15}{56}+ \frac{15}{56}[/tex]

= [tex]0.536[/tex]

= 53.6 5 %

Probability that he chooses two different types of biscuits is 53.65 %.

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Solve the equation 3/4x + 3 -2x = -1/4+1/2x+5
If necessary: Combine Terms
Apply Properties: Add, Subtract, Multiply, Divide

Answers

Answer:

x = -1

Step-by-step explanation:

3/4x + 3 -2x = -1/4 + 1/2x + 5

3/4x + 3 -2x = 19/4 + 1/2x

3x + 12 - 8x = 19 + 2x

-5x + 12 = 19 + 2x

-5x - 2x + 12 = 19

-7x = 19 - 12

-7x = 7

x = -1

By solving the algebraic equation  [tex]\frac{3}{4}x+3-2x = -\frac{1}{4}+ \frac{1}{2}x + 5[/tex], x = -1.

What is algebraic equation?

Algebraic equation is statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.

[tex]\frac{3}{4}x+3-2x = -\frac{1}{4}+ \frac{1}{2}x + 5\\\\\frac{3}{4}x-2x-\frac{1}{2}x = -\frac{1}{4}+5-3\\\\\frac{3x-8x-2x}{4} = \frac{-1+20 - 12}{4} \\\\-\frac{7x}{4} = \frac{7}{4}\\ \\ x = -1[/tex]

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58:27
The sequence below represents Marisa’s fine at the library for each day that she has an overdue book:

$0.50, $0.65, $0.80, $0.95, $1.10, ...

Which equation represents Marisa’s library fine as a function of a book that is n days overdue?

f(n) = 0.15n
f(n) = 0.50n
f(n) = 0.15n + 0.35
f(n) = 0.50n + 0.15

Answers

Answer:

a

Step-by-step explanation:

Helps me solve this problem please

Answers

Answer:

A.

Step-by-step explanation:

You just plug in the numbers

y = x - 7

-5 = 2 - 7

- 5 = - 5

This makes this equation true.

If 25⋅26=n, then which division equation is also true?



n÷26=25

26÷25=n

25÷n=26

25÷26=n

Answers

9514 1404 393

Answer:

  n÷26=25

Step-by-step explanation:

Starting with the equation ...

  25·26 = n

you can divide both sides of it by 26 to get ...

  25 = n ÷ 26 . . . . matches choice A

which table represents a nonlinear function? Help please!

Answers

The second one or the middle table mark Brainliest please
I think that the answer is the 2nd table

What is 40% of 60????

Answers

The answer: 40% of 60 is 24

Answer:  40% of 60 = 24

Determine the solution for x^2-3x-28=\> 0

Answers

Answer: x = -4 or x = 7

Step-by-step explanation:

x^2 - 3x - 28 =/>

(factor)

(x^2 + 4)(x-7) = 0

x + 4 = 0 or x - 7 = 0

(subtract -4 from 0 and 7 from 0)

x = -4 or x =7

Answer:

(infinity, -4] or [7, infinity).

Step-by-step explanation:

right on edge

john’s dog eats 4/5 tin of mince meat added in his meal every day . if dog eats 35 full tins of meat in one week(7 days) then how much does it eat every day.

Answers

Answer:

it eats five mince meat everyday

15+10f=-12 does someone knows this one?

Answers

Answer:

f = - 2.7

Step-by-step explanation:

15 + 10f = -12

10f = -12 - 15

f = -27/10

f = - 2.7

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Answers

NONONONONONONONONONONONONONONONONONONONONONONONONONONKNONONONONONONONONONONONONONONONONONONONONONONONONONONONONONONONONO
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Your grandfather is giving you $1000 to invest he has suggest an account there are 6% annual interest how much money will be the account 10 years from now

Answers

Answer:1600 dollars

Step-by-step explanation:

6% of 1000 is 60 then 60 × 10 is 600 so 1000 + 600 = 1600

solve for x.........

Answers

Answer:

61

Step-by-step explanation:

A triangle's total degrees is 180. You add the two angles they give you and then subtract the sum from 180. In number 9, the answer is 61. 47+72=119, 180-119= 61.

Find the solution for this system of equations:
y = -6x - 8
y = 46
O A) (24, -36)
OB) (36,-5)
OC) (46, -7)
OD) (-9. 46)

Answers

46=6x-8
+8 +8
54=6x
54/6=9
x=9

Nicholas found the 13th term of the geometric sequence 15, 30, 60, 120 the following way:
A(13) = 15 * 213
A(13) = 15 * 8,192
A(13) = 122,880

Is Nicolas correct? Why or why not? (Make sure to justify your answer) If Nicolas is incorrect please state the correct solution.

Answers

Answer: No. Nicolas is wrong.

Step-by-step explanation:

The formula for calculating nth term of a geometric sequence is given as:

= ar^n-1.

where a = first term = 15

r = common ratio = 30/15 = 2

n = 13

Using the formula,

= ar^n-1

= 15 × 2^(13-1)

= 15 × 2^12

= 15 × 4096

= 61440

The 13th term is 61440. Nicolas is wrong.

(Will mark brainliest and give $5 Starbucks digital card Include SC!!!) For which set of triangles can you immediately use the AAS congruence criteria to prove them congruent?(1 point)
1. triangles STU and VWX, where ∠T≅∠W, ∠U≅∠X, and SU≅VX

2. triangles GHI and JKL, where ∠G≅∠J, ∠H≅∠K, and GH≅JK

3. triangles MNO and PQR, where ∠N≅∠Q, MN≅PQ, and NO≅QR

Answers

I'm not so sure about this answer, but i remember doing something similar to this. I think it's 3.

A driver receives -25 points for a rule violation. What integer represents the change in points after four rule violations?

Answers

Answer:

It would be -100

MATH ANSWER IF YOU LIKE THESE SONGS
Muffin time
life is fun
i like trains

Answers

Answer:

1 + 1 = 2 - 3= maths

Step-by-step explanation:

yes dfuilwfjkwdlwo

Answer:

i like trains CHOOOOOO

Step-by-step explanation:

ANSWER NEEDED ASAP!
Find the value of x. (Hint: The sum of the angles in
a triangle is 180 degrees.)





The value of x is degrees.

Answers

Answer:

look below

Step-by-step explanation:

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees. Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

Basically since both sides have the same length which means that they will have the same angle degree (consist of the same side).
180-102 = 78
78/2=39
Answers is : x=39

Simplify

2 x m x n x 8​

Answers

16mn
Find the products of the numbers
And 16mn basically just means 16xmxn

The simplification for the given expression is 16mn.

What is an Algebraic expression?

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is as below,

2 x m x n x 8​

Since multiplication of two algebraic terms can be done by first multiplying their coefficients and then the variables.

Apply the above mentioned rule to get,

2 x m x n x 8​

= 2 x 8 ​x m x n

= 16 x m x n

= 16mn

Hence, the given expression is simplified as 2 x m x n x 8​ = 16mn.

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Find the slope of the line passing through the pair points (7,6) and (-7,-6)

Answers

Answer:

=6/7

Step-by-step explanation:

Convert 4/7 to 42nds

Answers

Answer:

24... I hoped dis helped.

75=-5(3+6m) I need this​

Answers

Are you finding m? If so here is the answer:

75 = -5(3 + 6m)

Distribute:
75 = -15 - 30m

Add 15 to both sides:
75 = -15 - 30m
+15 +15
90 = -30m

Divide by -30 on both sides:
90/-30 = (-30m)/-30

You should get: m = -3

PLS PLS PLS HELP THIS IS AN ALGEBRA 2 QUESTION

Answers

Answer:

look

Step-by-step explanation:

When she simplified her radical she put 5x*2x and 12 squared

what she should ahve done is 5x*4x^2 square 3x

please help me im dying help

Answers

Answer:

call 911 if you are in a emergency.

Answer:

c

Step-by-step explanation:

y = -5/2 + b (substitute the co-ordinates in y and x)

5 = -5/2 × (-2) + b

5 = 5 + b

b = 5-5

b = 0

I NEED HELP ASAP PLEASE

Answers

Answer:

Step-by-step explanation:

Yo when you get these kind of questions you can use desmos calculator, for the future.

is 0.5 or 17/34 greater

Answers

Answer:

They're equal; 17/34 as a decimal is 0.5

Step-by-step explanation:

Hope this helped, Have a Great Day!!

Answer:

17/34 is actually equal to 0.5. So since your comparing it to the decimal o.5 they are both equal to each other (:

Step-by-step explanation:

Thank you for your timeeee

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