What is the solution for -7x is less than or equal to 49

the graph shows the first five terms in a geometric sequence what is the iterative rule for the sequence

algol [13]

The iterative rule for the sequence is a_n = 8 · ( 0.5 )ⁿ ⁻ ¹

<h3>Further explanation</h3>

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

$\boxed{T_n = a + (n-1)d}$

$\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>d = common difference between adjacent numbers</em>

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

$\boxed{T_n = a ~ r^{n-1}}$

$\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}$

<em>Tn = n-th term of the sequence</em>

<em>Sn = sum of the first n numbers of the sequence</em>

<em>a = the initial term of the sequence</em>

<em>r = common ratio between adjacent numbers</em>

Let us now tackle the problem!

<u>Given:</u>

a₁ = 8

a₂ = 4

a₃ = 2

a₄ = 1

<u>Solution:</u>

<em>Firstly , we find the ratio by following formula:</em>

$r = a_2 \div a_1 = 4 \div 8 = 0.5$

$\texttt{ }$

<em>The iterative rule for the sequence:</em>

$a_n = a_1 \cdot~ r^{n-1}$

$a_n = 8 \cdot~ (0.5)^{n-1}$

$\texttt{ }$

<h3>Learn more</h3>

Geometric Series : brainly.com/question/4520950
Arithmetic Progression : brainly.com/question/2966265
Geometric Sequence : brainly.com/question/2166405

<h3>Answer details</h3>

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

6 0

3 years ago

X varies inversely as y^2, and x = 4 when y = 10. Find x when y = 2.

Ierofanga [76]

I believe it is A. x=16

6 0

3 years ago

Sophia is designing a piece of square art that must be four feet on each side. Which method could she use to most accurately det

prohojiy [21]

<span>Sophia could use a 10' long tape measure to measure the artwork. Would be The correct answer hope this helps</span>

4 0

3 years ago

Read 2 more answers

Description for this pair of angles

Setler [38]

Answer:

the answer is 29024280932

Step-by-step explanation:

easy

4 0

3 years ago

Anyone know this?? it’s finding the sine of a triangle!!

LenKa [72]

Answer:

I'm not sure what you want me to answer from this, so I solved for every variable:

Angle A: 83°

Side b: 6.29

Side c: 5.8

Step-by-step explanation:

-----Angle A:

Since the sum of the interior angles of a triangle ALWAYS equal 180°, we can solve for angle A as follows:

$A+51+46=180\\A+97=180\\A=83$

-----Side b:

Here, we use the sin rule for finding sides, since we know all of the angles as well as one side:

$\frac{a}{sin(A)} =\frac{b}{sin(B)} \\\frac{8}{sin(83)} =\frac{b}{sin(51)} \\8.06=\frac{b}{0.78} \\6.29=b$

-----Side c:

$\frac{a}{sin(A)} =\frac{c}{sin(C)} \\\frac{8}{sin(83)}=\frac{c}{sin(46)} \\8.06=\frac{c}{0.72} \\5.8=c$

7 0

2 years ago

Read 2 more answers