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4 years ago

A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?

Mathematics

1 answer:

ratelena [41]4 years ago

6 0

Answer:

f(1) = 31

Step-by-step explanation:

since f(n+1) -f(n) = -3

this sequence is arithmetic when the common diff is d= -3

the general term is :

f(n) = f(1) +(n-1)d

put n = 4

f(4) = f(1)+(4-1)(-3)

22 = f(1) - 9

f(1) = 31

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Rationalize the denominator of 1 /√3

seropon [69]

$\huge\sf\underline{\purple{❥}\pink{Q}\orange{U}\blue{E}\red{S}\green{T}\purple{I}\pink{O}\red{N}}$

rationalize the denominator of 1/√3

$\huge\sf\underline{\purple{❥}\pink{A}\orange {N}\blue{S}\red{W}\green{E}\purple{R}}$

$\frac{1}{ \sqrt{3} } \\ \\(to \: rationalize \: the \: denominator \\ we \: have \: multiply \: \frac{1}{ \sqrt{3} } \: to \: the \:given \: fraction \: \: \: ) \\ = \frac{1}{ \sqrt{3} } \times \frac{1}{ \sqrt{3} } \\ = ( \frac{1}{ \sqrt{3} } ) {}^{2} \\ = \frac{1}{3}$

HOPE IT HELPS YOU..

7 0

3 years ago

If the rate of inflation is 2.6% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following

PilotLPTM [1.2K]

Answer:

The current price of the item is $600.

The price of the item 9 years from today will be of $756.

Step-by-step explanation:

Price of the item:

The price of the item, in dollars, after t years, is given by:

$p(t) = 600(1.026)^t$

Current price of the item

This is p(0). So

$p(0) = 600(1.026)^0 = 600$

The current price of the item is $600.

9 years from today.

This is p(9). So

$p(9) = 600(1.026)^9 = 756$

The price of the item 9 years from today will be of $756.

3 0

3 years ago

What is 9+2x-18x+14y-10 simplified

algol13

Search it up on the calculater that is online it simplifies

5 0

4 years ago

Read 2 more answers

Classify each sequence as arithmetic, geometric or neither

Karolina [17]

Answer:

Geometric sequence = ⁵/9, ⁵/3, 5, 15, 45. . .

Arithmetic sequence = 16, 11, 6, 1, -4 . . .

Step-by-step explanation:

A geometric sequence is a sequence of numbers, in which every number in the sequence after the first term is multiplied by a common ratio, which gives us the next term. The common ratio is the ratio of a term to the term before it.

On the other hand, an arithmetic sequence is a sequence of number have a common difference between each consecutive terms. This common difference is gotten by subtracting a term from the term before it.

Now let's examine each sequence given:

==>16, 11, 6, 1, -4 . . .

11 - 16 = -5

6 - 11 = -5

1 - 6 = -5

-4 - 1 = -5

This is an arithmetic sequence. The commons difference "-5" is the same

==>⁵/9, ⁵/3, 5, 15, 45. . .

⁵/3 ÷ ⁵/9 = ⁵/3 × ⁹/5 = ⁹/3 = 3

5 ÷ ⁵/3 = ⁵ × ⅗ = 3

15 ÷ 5 = 3

45 ÷ 15 = 3

The common ratio "3" is the same. This is a geometric sequence.

3 0

3 years ago

How would the following problem be represented using colored tiles? -7 + (-3) seven red tiles plus three blue tiles seven red ti

Lelechka [254]

Answer:

Ok, we have the equation:

-7 + (-3)

Both numbers are negative, so the solution of this will be:

-7 + (-3) = -7 - 3 = -10.

Now, how we can represent it with tiles?

First we need to define, which tiles are the ones representing negative numbers?

We can use:

Red = positive

Blue = negative.

Then:

-7 is represented with seven blue tiles

-3 is represented with tree blue tiles

then:

(-7) + (-3)

will be represented with seven blue tiles, plus tree blue tiles.

When we add them, we have a total of 10 blue tiles, and as blue tiles represent negative numbers, 10 blue tiles is equal to -10.

5 0

3 years ago

Read 2 more answers

A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?​

A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?