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miss Akunina [59]

Is there supposed to be a picture I’m sorry I don’t see it

5 0

2 years ago

State whether each sequence is arithmetic and justify your answer. If the sequence is arithmetic, write a recursive and an expli

nasty-shy [4]

Answer:

Part A

$f(n)=52-12(n-1)$

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

$(2,4,8,16,32)\: \:$ Geometric Sequence

Part C

1/4,3/4,5/4,7/4,9/4

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)\\f(n)=\left\{\begin{matrix}1/4if \: \:n=1 & \\ f(n+1)+2/4& if\: n\geq 2 \end{matrix}\right$

Part D:

$h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right$

Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

$(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12$

Explicit Formula

To write an explicit formula is to write it as function.

$f(n)=52-12(n-1)$

Recursive Formula

To write it as recursive formula, is to write it as recurrence given to some restrictions:

$f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.$

Part B

$(2,4,8,16,32)\: \:$

Geometric Sequence, since 2*2=4 8*2=16 and 16*2=32 and 8+2=10 8+16=24

Part C

$(\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4})\\\$

Arithmetic Sequence, difference

$d=\frac{2}{4}$

Explicit Formula:

$g(n)=\frac{1}{4}+\frac{2}{4}(n-1)$

Recursive Formula

$g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.$

Part D

(1.1,1.5,1.9,2.3,2.7) Arithmetic Sequence, difference d=0.4

Explicit formula

$h(n)=1.1+0.4(n-1)\\$

Recursive Formula

$h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.$

6 0

3 years ago

What are the common multiples of 36 and 48

Vaselesa [24]

For 36 3 6 13. For 48 4 8 24. I think there are more but I can't think of them

7 0

3 years ago

What is the closed linear form of the sequence 3, 4, 5, 6, 7, ...?

Kay [80]

Answer:

Step-by-step explanation:

This is an arith. sequence.

The first term is 3 and the common difference is 1

Thus, the general formula for the nth term of this sequence is:

a(n) = 3 + 1(n - 1) This matches Answer A

6 0

3 years ago

Read 2 more answers

SAT scores: The College Board reports that in 2009, the mean score on the math SAT was 582 and the population standard deviation

Andrews [41]

Answer:

we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.

Step-by-step explanation:

H0 : μ = 582

H1 : μ < 582

Test statistic :

T = (xbar - μ) ÷ σ/√n

Xbar = 515 ; n = 20 ; σ = 120

T = (515 - 582) ÷ 120/√20

T = -67 / 26.832815

T = 2.50

Pvalue at t score = 2.50 ; df = 19 is 0.0187

At α = 0.0187

Pvalue > α ; Hence, we fail to reject the Null

Hence, we can conclude that there is no significant evidence to conclude that the mean score in 2010 differs from the mean score in 2009.

7 0

3 years ago

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