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2 years ago

Determine whether the following sequence is arithmetic, geometric, or neither.

Mathematics

1 answer:

lawyer [7]2 years ago

5 0

Answer:

arith

Step-by-step explanation:

Let's check whether or not this is a geometric series.

The first term is 1 1/3, or 4/3.

What would the common ratio be, to convert this 4/3 into the 2nd term, 2?

(4/3)r = 2, or r = 2(3/4) = 6/4 = 3/2.

Assuming that the common ratio is r = 3/2, will multiplying 2 by 3/2 result in the 3rd term, 2 2/3? NO. So this is NOT a geometric progression.

The difference between 1 1/3 and 2 is 2/3. If we add 2/3 to 2, we get 2 2/3, which agrees with the given 3rd term.

If we add 2/3 to 2 2/3, do we get the fourth given term, 3 1/3?

2/3 + 2 2/3 is equivalent to 2 4/3, or 10/3, which is equivalent to 3 1/3.

Thus, this IS an arithmetic sequence, and the common difference is 2/3.

You might be interested in

The length of a rectangle exceeds its breadth by 7cm. if the length is decreased by 4cm and the breadth is increased by 3cm, the

riadik2000 [5.3K]

Answer:

16cm

Step-by-step explanation:

Let the breadth = x

The length exceeds = x + 7

The breadth increased = x + 3

Because it said the length decreased by 4 so, the length would be:

x + 7 - 4 = x + 3

Original area:

We learn that:

area = length * breadth

x*(x+7) = (x+3)*(x+3)

x^2 + 7x = (x+3)^2

x^2 + 7x = x^2 + 6x + 9 (We also learn that (a+b)^2 = a^2 + 2ab + b^2

x^2 - x^2 + 7x - 6x = 9

x = 9 (so the breadth = 9)

The length = x + 7 = 9+7 = 16(cm)

Hope this help you :3

7 0

2 years ago

URGENT PLEASE ANSWER THESE

Dimas [21]

Answer:

1A) 2 gallons of 20% solution and 3 gallons 15% solution needed

1B) 4 gallons of 20% solution and 1 gallons 15% solution needed

Step-by-step explanation:

1A) adding 20% salt and 15% water making 5 gallons of 17%

20% salt + 15% salt = 5 gallons of 17% salt

0.20x + 0.15(5 - x) = 0.17(5)

0.20x + 0.75 - 0.15x = 0.85

0.20x + 0.75 - 0.75 - 0.15x = 0.85 - 0.75

0.20x - 0.15x = 0.10

0.05x = 0.10

0.05x/ 0.05 = 0.10/0.05

x = 2 gallons (amount of 20% solution needed)

5 - x = 5 - 2 = 3 gallons (amount of 15% solution needed)

1B)

0.20x + 0.15(5 - x) = 0.19(5)

0.20x + 0.75 - 0.15x = 0.95

0.20x + 0.75 - 0.75 - 0.15x = 0.95 - 0.75

0.20x - 0.15x = 0.20

0.05x = 0.20

0.05x / 0.05 = 0.20/0.05

x = 4 gallons (amount of 20% solution needed)

5 - x = 5 - 4 = 1 gallons (amount of 15% solution needed)

Learn more about System of Equations here: brainly.com/question/12526075

4 0

1 year ago

Hello I was wondering if someone would help me with this tricky question?

Rudiy27

Answer:

The two coordinates should be (6, 3) and (10, 4).

Step-by-step explanation:

rise / run

y-value of the 2nd coordinate = 3 + 1 = 4

x-value of the 2nd coordinate = 6 + 4 = 10

The two coordinates should be (6, 3) and (10, 4).

7 0

2 years ago

You have a $3175 student loan. Suppose you pay the loan off in two and a half years (30 months). Estimate your monthly payment b

finlep [7]

Answer:

$106

Step-by-step explanation:

The formula given for Monthly payment of a loan =

P × [ r (1 + r)/(1 + r)^n - 1

Where

r = interest rate

n = number of monthly payments

P = Present value of the loan

From the question,

r = interest rate, we were told to ignore hence, r = 0

P = $3,175

n = 30

Hence,

Amount to be paid monthly = P/n

= $3175/30

= $105.83

Approximately to the nearest dollars

= $106

6 0

2 years ago

If x = a sin α, cos β, y = b sin α.sin β and z = c cos α then (x²/a²) + (y²/b²) + (z²/c²) = ?

Oduvanchick [21]

$\large\underline{\sf{Solution-}}$

Given:

$\rm \longmapsto x = a \sin \alpha \cos \beta$

$\rm \longmapsto y = b \sin \alpha \sin \beta$

$\rm \longmapsto z = c\cos \alpha$

Therefore:

$\rm \longmapsto \dfrac{x}{a} = \sin \alpha \cos \beta$

$\rm \longmapsto \dfrac{y}{b} = \sin \alpha \sin \beta$

$\rm \longmapsto \dfrac{z}{c} = \cos \alpha$

Now:

$\rm = \dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} }$

$\rm = { \sin}^{2} \alpha \cos^{2} \beta + { \sin}^{2} \alpha \sin^{2} \beta + { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha (\cos^{2} \beta + \sin^{2} \beta )+ { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha \cdot1+ { \cos}^{2} \alpha$

$\rm = { \sin}^{2} \alpha + { \cos}^{2} \alpha$

$\rm = 1$

Therefore:

$\rm \longmapsto\dfrac{ {x}^{2} }{ {a}^{2}} + \dfrac{ {y}^{2} }{ {b}^{2} } + \dfrac{ {z}^{2} }{ {c}^{2} } = 1$

5 0

2 years ago