All categories

2 years ago

In an arithmetic sequence, a1=5 and a6=-5. Determine an equation for an, the nth term of this sequence.

Mathematics

1 answer:

GalinKa [24]2 years ago

6 0

Answer: 7 - 2n

Step-by-step explanation:

a1 = 5

a6 = -5 = a + (n - 1)d = a + (6 - 1)d

a + 5d = -5

Since a1 = 5

5 + 5d = -5

5d = -5 - 5

5d = -10

d = -10/5

d = -2

Therefore, the equation to calculate the nth term of this sequence will be:

= a + (n-1)d

= a + (n - 1)-2

= 5 -2n +2

= 7 - 2n

You might be interested in

What is the value of X

andreev551 [17]

Answer:

vfhgfhfjhfvhjgv

Step-by-step explanation:

6 0

2 years ago

Doug split a pack of cards so that he and his friends each got 6 cards. If there were 24 cards in the pack, how many friends did

GuDViN [60]

Answer:

Step-by-step explanation:

24 divided by 6 is 4, subtract Doug, there were 3 friends

4 0

2 years ago

If As income is 20% more than Bs income, how much percent is Bs income less than As income

vitfil [10]

$As\ is\ 120\%\ Bs\\\\120\%=1.2\to\frac{As}{Bs}=1.2\\\\\frac{As}{Bs}=\frac{12}{10}\to\frac{Bs}{As}=\frac{10}{12}\to\frac{Bs}{As}=\frac{5}{6}\\\\\frac{5}{6}\cdot100\%=\frac{500}{6}\%=83\frac{1}{3}\%\\\\100\%-83\frac{1}{3}\%=16\frac{2}{3}\%\\\\Answer:Bs\ income\ is\ 16\frac{2}{3}\%\ less\ than\ As\ income.$

6 0

2 years ago

A car rental costs $32 as a base fee, plus $28 per day. Use the explicit rule f (n )= 28n + 32

alexdok [17]

Answer:

The charges paid for the first four days are:

$144.

Step-by-step explanation:

To obtain the charges paid for the first 4 days, you must use the given explicit rule given:

f (n) = 28n + 32

Where:

n = Number of days the person rents the car.

As we need to obtain the charges to 4 days, we replace this value in the explicit rule:

f (n) = 28n + 32
f (4) = 28(4) + 32
f (4) = 112 + 32
f (4) = 144

With these calculations, you can identify the charges paid for the first 4 days are $144, where $112 is the money by each day of the four days and $32 is the base fee.

3 0

2 years ago

On a certain hot summer day, 481 people used the public swimming pool. The daily prices are 1.25 for children and 2.25 for adult

spayn [35]

Answer:the number of children that swam in the public pool that day is 222

the number of adult that swam in the public pool that day is 259

Step-by-step explanation:

Let x represent the number of children that swam in the public pool that day.

Let y represent the number of adult that swam in the public pool that day.

On a certain hot summer day, 481 people used the public swimming pool. This means that

x + y = 481

The daily prices are 1.25 for children and 2.25 for adults. The receipts for admission totaled to 86.25. This means that

1.25x + 2.25y = 860.25 - - - - - - - -1

Substituting x = 481 - y into equation 1, it becomes

1.25(481 - y) + 2.25y = 860.25

601.25 - 1.25y + 2.25y = 860.25

- 1.25y + 2.25y = 860.25 - 601.25

y = 259

Substituting y = 259 into x = 481 - y, it becomes

x = 481 - 259

x = 222

8 0

3 years ago