Espress the following in standard form 24.12

An arithmetic sequence is defined by the general term tn = -5 + (n - 1)78, where n ∈N and n ≥ 1. What is the recursive formula o

Gnoma [55]

Answer:

C

Step-by-step explanation:

In general for arithmetic sequences, recursive formulas are of the form

aₙ = aₙ₋₁ + d,

and the explicit formula (like tₙ in your problem), are of the form

aₙ = a₁ + (n - 1)d,

where d is the common difference. So converting between the two of these isn't so bad. In this case, your problem wants you to have an idea of what t₁ is (well, every answer says it's -5, so there you are) and what tₙ₊₁ is. Using the formulas above and your given tₙ = -5 + (n - 1)78, we can see that the common difference is 78, so no matter what we get ourselves into, the constant being added on at the end should be 78. That automatically throws out answer choice D.

But to narrow it down between the rest of them, you want to use the general form for the recursive formula and substitute (n + 1) for every instance of n. This will let you find tₙ₊₁ to match the requirements of your answer choices. So

tₙ₊₁ = t₍ₙ₊₁₎₋₁ + d ... Simplify the subscript

tₙ₊₁ = tₙ + d

Therefore, your formula for tₙ₊₁ = tₙ + 78, which is answer choice C.

6 0

2 years ago

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Ben had a coupon for an additional 15% off of the sale price of any intem in a store. He uses his coupon to buy a shirt whose sa

borishaifa [10]

Answer:

3

Step-by-step explanation:

15% of 20=0.15 x 20=3

4 0

2 years ago

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last year 1/5 of the students in your class played a sport this year 10 students join the class five of the new students play a

tino4ka555 [31]

Answer:

60

Step-by-step explanation:

last year 1/5 of the class played sports, so s = (1/5) c

the next year, s increased by 5, c increased by 10 and the fraction changed to 1/4, so for the next year (s+5) = (1/4)(c+10)

To solve this we can substitute s = (1/5)c from the first equation into the second, so

((1/5)c + 5)=(1/4)(c+10), simplify both sides

(1/5)c + 5 = (1/4)c + 10/4, simplify 10/4 to 5/2

(1/5)c + 5 = (1/4)c + 5/2, multiply both sides by 20 to eliminate fractions (least common multiple of 2, 4 and 5)

4c + 100 = 5c + 50, subtract 4c, subtract 50 from both sides

50 = c, number of students in class last year was 50, this year is 10 more, so this year is 60

5 0

2 years ago

Tom planted 1/2 of an 8-ft by 9-ft garden with vegetables. He planted tomatoes in 1/3 of the vegetable garden and corn in the re

ser-zykov [4K]

Answer:

Corn was planted in 24 sq.ft. of the vegetable garden.

Step-by-step explanation:

Length of garden = 9 ft

width of garden = 8 ft

Hence we will first find the total area of garden.

Total area of garden = length × width = $8 \times 9 = 72ft^2$

He planted 1/2 of the garden with vegetables.

Hence.

Area of Vegetables garden = $\frac{1}{2}\times \textrm{Total Area of Garden} = \frac{1}{2}\times 72 = 36ft^2$

He planted tomatoes in 1/3 of the vegetable garden and corn in the rest

Area in which tomatoes was planted = $\frac{1}{3}\times \textrm{Area of Vegetables Garden} = \frac{1}{3}\times 36 = 12ft^2$

Hence Area in which corn were planted = Area of Vegetables garden - Area in which tomatoes was planted = $36ft^2-12ft^2=24ft^2$

Hence Area of vegetable garden in which corn was planted is 24 sq.ft.

7 0

2 years ago

5/6+2/9= in simplest form I NEED this plz help

tensa zangetsu [6.8K]

Answer: 1 1/18

Step-by-step explanation: 5/6 + 2/9 I know this might seem like common, but the Numerator is the top number of a fraction and the Denominator is the bottom a fraction. When the numerator and the denominator are the same such as 5/5 the fraction equals one (I know its real fancy). When you're multiplying a fraction that equals on by another fraction its really just multiplying by a fancy looking 1 that's disguised as a fraction such as 5/5. If you simplify it it goes to the fraction it was as long it was simplified to the max (5/5 x 1/2 = 5/10= 1/2)

First, you need to find a like denominator, which is 18

Then, you got to multiply each fraction to make them have common denominators ...multiply 5/6 by 3/3 ( 3/3 is just a fancy way of saying one) 5/6 x 3/3 = 15/18....multiply 2/9 by 2/2 (which is just another fancy way of saying one ) 2/9 x 2/2=4/18
Next you add them but only the numerator 15/18 + 4/18 = 19/18
Finally, you change the the fraction into a mixed number 1 and 1/18

6 0

2 years ago

Espress the following in standard form 24.12​

Espress the following in standard form 24.12