If f:x =

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

Find the measure of LaTeX: aa and LaTeX: b\:bin the diagram below.

Fudgin [204]

Answer:

what is LaTeX

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers

An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, t

Alenkinab [10]

Answer:

The triangle's perimeter is 61.77 inches.

Step-by-step explanation:

Since an altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles, and as a result, the altitude cuts the base into two equal segments, and the length of the altitude is 26 inches, and the length of the base is 9 inches, to find the triangle's perimeter the following calculation must be performed:

Isosceles triangle = 2 equal sides

To obtain the value of the sides, the Pythagorean theorem must be applied on the right triangle formed with the altitude.

(9/2) ^ 2 + 26 ^ 2 = X ^ 2

4.5 ^ 2 + 26 ^ 2 = X ^ 2

20.25 + 676 = X ^ 2

√ (20.25 + 676) = X

√696.25 = X

26.38 = X

26.3865 x 2 + 9 = X

52.77 + 9 = X

61.77 = X

Therefore, the triangle's perimeter is 61.77 inches.

5 0

3 years ago

How do you calculate 278 × 11 using estimation?

neonofarm [45]

Answer:

2800

Step-by-step explanation:

round 278 to 280

then round 11 to 10

then times the 2 answers together

8 0

3 years ago

Read 2 more answers

A microwave oven costs $124. 85 before it is marked down. If it is marked down by 63%, what is its new price, to the nearest cen

Nuetrik [128]

Answer:

d. 46.19

Step-by-step explanation:

y=124.85(0.37)

to figure out the percent decrease, subtract the percent from 100. then divide by 100 to get a decimal. multiply that decimal by the original cost to get the answer.

5 0

2 years ago