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
klasskru [66]
2 years ago
14

PLEASE HELP!!!!! 3, 8, 13, 18, 23, .... The recursive formula for this sequence is:

Mathematics
1 answer:
rodikova [14]2 years ago
8 0

Answer:

a₈ = 37

Step-by-step explanation:

The given arithmetic sequence is: 3, 8, 13, 18, 23, . . .

The recursive formula for the sequence is: $ a_n = a_{n - 1} + 5 $

Here, $ a_n $ represents the $ n^{th} $ of the sequence.

And, $ a_{n - 1} $ represents the $ (n - 1)^{th} $ of the sequence.

'+5' denotes that '5' is added to the $ (n - 1)^{th} $ term to get the $ n^{th} $ term. In other words, the difference between two consecutive numbers in the sequence is 5.

Now, we are asked to find a₈ i.e., n =8.

Substituting in the recursive formula we get: a₈ = a₍₈₋ ₁₎ + 5 = a₇ + 5.

So, to determine a₈ we need to know a₇. From the sequence we see that a₅ = 23.

⇒ a₆ = 23 + 5 = 28.

⇒ a₇ = 28 + 5 = 32.

⇒ a₈ = 32 + 5 = 37.

Therefore, the $ 8^{th} $ term of the sequence is 37.

You might be interested in
How can I Factor 7 + 14x ??
wariber [46]

Answer: 7(1+2x)

Step-by-step explanation:

7 and 14 can be divided by 7. As a result, you take 7 out and bam!

6 0
3 years ago
Find the lateral area of the square pyramid shown, to the nearest whole number.
mylen [45]
I believe the correct answer is D)
3 0
3 years ago
Read 2 more answers
How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y
son4ous [18]

Solution:

Given:

x^2=6y

Part A:

The vertex of an up-down facing parabola of the form;

\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}

Rewriting the equation given;

\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\  \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\  \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\  \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\  \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}

Therefore, the focus is;

(0,\frac{3}{2})

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

\begin{gathered} 4p(y-k)=(x-h)^2 \\  \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}

Rewriting the equation in standard form,

\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}

Therefore, the directrix is;

y=-\frac{3}{2}

3 0
11 months ago
What number is being factored in this factor tree? <br><br>A.72<br> B.180 <br>C.216<br> D.324
Tatiana [17]

Answer:

not sure if it's ryt but I think it's A

7 0
3 years ago
Help me plzzzzzzz guyssss
maks197457 [2]

Answer:

1. 75%

2. 20%

3. 20%

4. decrease 5.4%

Step-by-step explanation:

1. 119-68=51, 51/68=0.75

2. 30-24=6, 6/30=0.20

3. 18-15=3, 3/15=0.20

4. 762-721=41, 41/762=0.0538

5 0
2 years ago
Other questions:
  • Melcher used 24% if the memory card on his digital camera while taking pictures at a family reunion. If melcher took 96 pictures
    11·1 answer
  • Find all the angle measures for the quadrilateral
    8·2 answers
  • 88 less than 8 times a number is 34 less than twice. turn to equation
    13·1 answer
  • What number must be added to the expression below to complete the square? x2 - 11x
    7·2 answers
  • Answer number 12 please
    13·1 answer
  • What is another name for 23 ten thousands?
    15·1 answer
  • What is the smallest number of squares into which you can divide a rectangle with dimensions 6×7?
    15·1 answer
  • 1. Complete the statements to describe ratios.
    12·1 answer
  • What is the measure of angle y?
    5·2 answers
  • Find the volume of the cylinder. Round your answer to the nearest tenth. 15 m 5 m The volume of the cylinder is about cubic mete
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!