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
frutty [35]
1 year ago
14

Please help me find the answers to all the questions whoever answers all the question I will mark the brainlest.

Mathematics
1 answer:
Alex73 [517]1 year ago
7 0

Answer:

\textsf{a)} \quad \textsf{Recursive Rule}: \quad a_n=5n-2

     \textsf{Explicit Rule}: \quad \begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}

b)  4998

c)  explicit rule (see below for explanation)

d)  see below

Step-by-step explanation:

An explicit formula for an <u>arithmetic sequence</u> allows you to find the nth term of the sequence.

A recursive formula for an <u>arithmetic sequence</u> allows you to find the nth term of the sequence <em>provided </em>you know the value of the previous term in the sequence.

<h3><u>Part a</u></h3>

<u>Explicit Formula</u>

a_n=a+(n-1)d

where:

  • a_n is the nth term
  • a is the first term
  • n is the number of the term
  • d is the common difference

<u>Given sequence</u>:  3, 8, 13, 18, 23, ...

To find the <u>common difference</u>, subtract one term from the next term.

Therefore:

  • a = 3
  • d = 8 - 3 = 5

Substituting the found values of a and d into the formula to create a explicit rule for the given sequence:

\implies a_n=3+(n-1)5

\implies a_n=3+5n-5

\implies a_n=5n-2

<u>Recursive Formula</u>

a_n=a_{n-1}+d \quad \textsf{for }n\geq 2

where:

  • a_n  is the nth term
  • a_{n-1} is the term immediately before the nth term
  • d is the common difference

We already know the common difference our previous calculations.

Therefore:

\implies a_n=a_{n-1}+5

When giving a recursive rule we also have to define the <u>first term</u> of the sequence, as it is not part of the formula.  Therefore, the full recursive rule for the given sequence is:

  \begin{cases}a_1=3\\a_n=a_{n-1}+5\end{cases}

<h3><u>Part b</u></h3>

To find the 1000th term of the sequence, use the <u>explicit rule</u> and substitute n = 1000:

\implies a_{1000}=5(1000)-2

\implies a_{1000}=5000-2

\implies a_{1000}=4998

Therefore, the 1000th term of the sequence is 4998.

<h3><u>Part c</u></h3>

We used the explicit rule to find the 1000th term as this rule allows us to find the nth term of the sequence <em>without </em>having to know any previous terms.

<h3><u>Part d</u></h3>

The <u>disadvantage</u> of a recursive rule when compared to an explicit rule is that we need to know the <u>previous term</u> to find the nth term, whereas the explicit rule doesn't need this information.

Learn more about sequences here:

brainly.com/question/27924553

brainly.com/question/27775450

You might be interested in
I’ll give brainliest
Brilliant_brown [7]

Answer:

B

Step-by-step explanation:

We know that it costs 37 cents to mail a letter that weighs 1 oz or less. This would mean that for x ≤ 1, P(x) should equal 37. Already, we can eliminate A and D.

We also know that it costs an additional 26 cents for at most another ounce added to the original 1 ounce. This means that for 1 < x ≤ 2, P(x) = 26 + 37 = 63. This is shown by B.

Thus, the answer is B.

<em>~ an aesthetics lover</em>

5 0
3 years ago
The smaller triangle was dilated to form the larger triangle what is the value of x
Sladkaya [172]

Answer:

i think c which is 14

3 0
3 years ago
Find the volume of the pyramid below.<br> 7.2 in<br> 9.7 in
kumpel [21]

Answer:

23.28 inches (im not sure if this is correct because you need length, height, and width.)

Step-by-step explanation:

<u>lwh</u>

3

4 0
2 years ago
Can this be simplified?
liraira [26]
No Nothing Further Can Be Done
6 0
3 years ago
Read 2 more answers
Rolling a number less than 4 on a standard number cube *
Molodets [167]
I think it would be a
4 0
3 years ago
Other questions:
  • if a lawyer bills $350/hour, how much does he makes every second? how much does he make per year? assume he works 50 hours per w
    6·1 answer
  • When multiplying a decimal do you move it forward or backward
    9·1 answer
  • What is one area students do not need to review when they're preparing for the arithmetic section of ACCUPLACER?
    7·1 answer
  • Which are correct representations of the inequality 6x2 3 + 4(2x - 1)?
    14·1 answer
  • Solve equation <br> 91=7(7+2r)
    14·2 answers
  • Which graph represents the function y = 4?
    14·1 answer
  • Please help me with whole answer i give brainliest.
    11·1 answer
  • Brainliest for whoever gets this right
    11·1 answer
  • 1. 6x - 29 = 115<br> 2. 3y - 1 = 29<br> 3. 4z - 32 = 36<br><br> find x, y, and z
    10·1 answer
  • an elderly patient goes to a general doctor every 4 weeks and goes to a chiroprator every 6 weeks . if he went to both the gener
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!