All categories

3 years ago

the first term of an arthimetic sequence is 42 the rule an= an-1 +8 can 1 can be used explain how to write explict rules

Mathematics

2 answers:

choli [55]3 years ago

7 0

Answer:

$a_{n}$ = 8n + 34

Step-by-step explanation:

The explicit rule for an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given the recursive rule

$a_{n}$ = $a_{n-1}$ + 8

where + 8 is the common difference d , then

$a_{n}$ = 42 + 8(n - 1) = 42 + 8n - 8 = 8n + 34

Explicit rule is

$a_{n}$ = 8n + 34

Svet_ta [14]3 years ago

3 0

Answer:

34 + 8n

Step-by-step explanation:

a₁ = 42

$a_{n} = a_{n-1} + 8$

a₂ = a₁ + 8 = 42 + 8 = 50

a₃ = a₂ + 8 = 50 + 8 = 58

a₄ = a₃ + 8 = 58 + 8 = 66

Arithmetic sequence: 42, 50 , 58 , 66, ......

a₁ = 42 ; d = 8

$a_{n}$ = a₁ + d(n-1)

= 42 + 8(n - 1)

= 42 + 8n - 8

= 34 + 8n

You might be interested in

What are the possible outcomes?

vesna_86 [32]

Answer:

A= X,B

B= L,G

C= M,W

The total number of combinations is 12

6 0

3 years ago

seven different gifts are to be distributed among 10 children. How many distinct results are possible if no child is to receive

Alik [6]

Answer:

120 distinct results are possible if no child is to receive more than one gifts.

Step-by-step explanation:

When the order is not important, we use the combination formula:

$C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The order is said to be not important if for example, John receiving the Buffalo Bills jersey and then Laura receiving the Cleveland Browns jersey is the same as Laura receiving the Cleveland Browns jersey before John receives the Buffalo Bills jersey.

In this problem, we have that:

Combinations of 7 from a set of 10 elements. So

$C_{n,x} = \frac{n!}{x!(n-x)!}$

$C_{10,7} = \frac{10!}{7!(3)!} = 120$

120 distinct results are possible if no child is to receive more than one gifts.

6 0

3 years ago

[30 POINTS] Please help!!!

Len [333]

Answer:

Part 1) $y=1.5x+5$

Part 2) $y=-(2/3)x-(11/3)$

Part 3) $y=0.25x+2.75$

Part 4) $y=-2x+5$

Part 5) $y=0.5x-1$

Part 6) The graph in the attached figure

Step-by-step explanation:

Part 1) we have

$m=3/2=1.5$

$point(-2,2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-2=1.5(x+2)$

$y=1.5x+3+2$

$y=1.5x+5$

Part 2) we know that

If two lines are perpendicular

then

the product of their slopes is equal to minus one

$m1*m2=-1$

the slope of the line 1 is equal to

$m1=1.5$

Find the slope m2

$1.5*m2=-1$

$m2=-2/3$

Find the equation of the line 2

we have

$m2=-2/3$

$point(-7,1)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-1=(-2/3)(x+7)$

$y=-(2/3)x-(14/3)+1$

$y=-(2/3)x-(11/3)$

Part 3) we have

$m=1/4=0.25$

$point(1,3)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y-3=0.25(x-1)$

$y=0.25x-0.25+3$

$y=0.25x+2.75$

Part 4) we have

$m=-2$

$b=5$ -----> y-intercept

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

substitute the values

$y=-2x+5$

Part 5) we have that

The slope of the line 4 is equal to $-2$

the slope of the line perpendicular to the line 4 is equal to

$-2*m=-1\\m=(1/2)=0.5$

therefore

in this problem we have

$m=0.5$

$point(-2,-2)$

The equation of the line into point slope form is equal to

$y-y1=m(x-x1)$

substitute

$y+2=0.5(x+2)$

$y=0.5x+1-2$

$y=0.5x-1$

Part 6)

using a graphing tool

see the attached figure

3 0

3 years ago

Joan wants to set a 4-digit unlock code for her mobile phone. She plans to use only odd numbers and to make sure that no number

LuckyWell [14K]

Answer: 120

Step-by-step explanation:

There are 5 digits that are odd, 1 3 5 7 9

There are 5 possibilities for the first digit, 4 for the second, 3 for the third, and 2 for the last, so there are 5 x 4 x 3 x 2 = 120

6 0

1 year ago

Please do #4 It’s it the one on the bottom

spin [16.1K]

We need to graph this equation:

$16x+2y=300$

Its solutions are the points through which it graph passes. Since it's a linear equation its graph is a straight line and we only need two of its points to draw it. But before graphing let's re-write the equation. We can substract 16x from both sides:

$\begin{gathered} 16x+2y=300 \\ 16x+2y-16x=300-16x \\ 2y=300-16x \end{gathered}$

And we divide both sides by 2:

$\begin{gathered} \frac{2y}{2}=\frac{300-16x}{2}=\frac{300}{2}-\frac{16x}{2} \\ y=150-8x \end{gathered}$

So now with this equation if we pick two random x values we'll get their corresponding y values. This way we'll find two points that are part of the graph which is the line that passes through both. We can begin with x=0:

$y=150-8\cdot0=150$

So the first point is (0,150). Then we can take x=10 and we get:

$y=150-8\cdot10=150-80=70$

So the second point is (10,70). Then the graph is the line that passes through points (0,150) and (10,70). In order to represent it

3 0

1 year ago