1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andreyandreev [35.5K]
2 years ago
14

This math my graduation depends on it

Mathematics
1 answer:
In-s [12.5K]2 years ago
7 0

In an arithmetic sequence, consecutive terms have a fixed distance d between them. If a₁ is the first term, then

2nd term = a₂ = a₁ + d

3rd term = a₃ = a₂ + d = a₁ + 2d

4th term = a₄ = a₃ + d = a₁ + 3d

and so on, up to

nth term = a_n = a_{n-1} + d = a_{n-2} + 2d = a_{n-3} + 3d = \cdots = a_1 + (n-1)d

so that every term in the sequence can be expressed in terms of a₁ and d.

6. It's kind of hard to tell, but it looks like you're given a₁₃ = -53 and a₃₅ = -163.

We have

a₁₃ = a₁ + 12d = -53

a₃₅ = a₁ + 34d = -163

Solve for a₁ and d. Eliminating a₁ and solving for d gives

(a₁ + 12d) - (a₁ + 34d) = -53 - (-163)

-22d = 110

d = -5

and solving for a₁, we get

a₁ + 12•(-5) = -53

a₁ - 60 = -53

a₁ = 7

Then the nth term is recursively given by

a_n = a_{n-1}-5

and explicitly by

a_n = 7 + (n-1)(-5) = 12 - 5n

7. We do the same thing here. Use the known terms to find a₁ and d :

a₁₉ = a₁ + 18d = 15

a₃₈ = a₁ + 37d = 72

⇒   (a₁ + 18d) - (a₁ + 37d) = 15 - 72

⇒   -19d = -57

⇒   d = 3

⇒   a₁ + 18•3 = 15

⇒   a₁ = -39

Then the nth term is recursively obtained by

a_n = a_{n-1}+3

and explicitly by

a_n = -39 + (n-1)\cdot3 = 3n-42

8. I won't both reproducing the info I included in my answer to your other question about geometric sequences.

We're given that the 1st term is 3 and the 2nd term is 12, so the ratio is r = 12/3 = 4.

Then the next three terms in the sequence are

192 • 4 = 768

768 • 4 = 3072

3072 • 4 = 12,288

The recursive rule with a₁ = 3 and r = 4 is

a_n = 4a_{n-1}

and the explicit rule would be

a_n = 3\cdot4^{n-1}

You might be interested in
I NEED THE ANSWER TO THIS QUESTION ASAP
ra1l [238]

Answer:

B

Step-by-step explanation:

Add 15,181 and 137 then for part b subtract 15,181 and 4,893 and that's a way higher number than 4,893 and 137

8 0
1 year ago
Read 2 more answers
Which of the following functions is graphed below
sleet_krkn [62]

Answer:

A.

Step-by-step explanation:

8 0
3 years ago
In the first week
FromTheMoon [43]

The percent change in the number of people who went to the pool

between the first  and last week is 10% less

Step-by-step explanation:

The given is:

  • In the first week  of July, a record 1,060 people went to the local  swimming pool
  • In the second week, 105 fewer  people went to the pool
  • In the third week, 135  more people went to the pool than in the second  week
  • In the fourth week, 136 fewer people  went to the pool than in the third week

We need to find the percent change in the number of  people who

went to the pool between the first  and last weeks

∵ There were 1060 people in the 1st week

∵ There were 105 fewer people in the 2nd week

∴ The number of people in the 2nd week = 1060 - 105 = 955

∴ There were 955 people in the 2nd week

∵ There were 135 more people in the 3rd week than the 2nd week

∵ There were 955 people in the 2nd week

∴ The number of people in the 3rd week = 955 + 135 = 1090

∴ There were 1090 people in the 3rd week

∵ There were 136 fewer people in the 4th week than in the 3rd week

∵ There were 1090 people in the 3rd week

∴ The number of people in the 4th week = 1090 - 136 = 954

∴ There were 954 people in the 4th week

Let us find the change from 1st week to last week

∵ There were 1060 people in the 1 st week

∵ There were 954 people in the last week

∴ The change = 1060 - 954 = 106

∵ Percent change = \frac{Change}{Original} × 100%

∴ Percent change = \frac{106}{1060} × 100%

∴ Percent change = 10%

The percent change in the number of people who went to the pool

between the first  and last week is 10% less

Learn more:

You can learn more about percentage in brainly.com/question/12501490

#LearnwithBrainly

8 0
3 years ago
Early one October, you go to a pumpkin patch to select your Halloween pumpkin. You lift the 3.4kg pumpkin to a height of 1.4m ,
Snezhnost [94]
Work equals force times distance. In this case, work equals mgh (mg is the force and h is the distance. Solving the equation W = mgh gives you W = (3.4 kg)(9.8 m/s^2)(1.4 m) = 47 J (joules).
3 0
3 years ago
An isosceles trapezoid is a trapezoid with congruent legs. true or false?
Neko [114]

Answer:

True.

Step-by-step explanation:

The sides are legs and that's what makes it isosceles.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Write the subtraction sentence that has a difference of 10
    15·2 answers
  • Find the value for b.<br> 3x^2– X – 10 = 0<br> Entor the correct answer
    7·2 answers
  • Translate the following argument in a standard form categorial syllogims then use venn diagram or rules for syllogim to determin
    15·1 answer
  • Janet rents a car while spending her vacation traveling in New Zealand. When she returns the car, she has driven 925 miles and u
    15·1 answer
  • What is h less than 30 algebraic expretion
    12·1 answer
  • Y’all please help on these 2 questions !! asap
    8·1 answer
  • The square of the product of 4 and a number.
    15·2 answers
  • Arush is reading a pop-up book. When the book is open to an angle of 105°, the wizard's wand is waving
    7·1 answer
  • A product has five factors. Three factors are negative integers and two factors are positiv
    6·1 answer
  • 1 3 x+ - 6 y = - 2/3 * x + 3
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!