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Veseljchak [2.6K]
3 years ago
13

Which function describes the arithmetic sequence shown -1, 1, 3, 5, 7, 9, 11, 13, ...

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
7 0

Answer:

f(n) = 2n - 3 describes the arithmetic sequence,

-1, 1, 3, 5, 7, 9, 11, 13,.......

Step-by-step explanation:

Function:

A function is like a machine that gives an output for a given input.

A function has an independent variable which is called the input of the function.

The output for a given input is called the dependent variable.

Here. 'n' is the independent variable

f(n) is the function dependent variable i.e function of n as an output.

For Arithmetic sequence

a_{n}= a_{1} + (n-1)d

Where

a_{n} = nth number of the sequence.

a₁ = First term

d = common difference = a₂ - a₁ = a₃ - a₂ = so on

For a function which describes Arithmetic sequence,

a₁ = -1

d = 1 - -1 =2

∴ f(n) = a₁ + (n -1 )d

substituting the values we get

∴ f(n) = -1 +(n-1)2

using distributive property

∴ f(n) = - 1 +  2n - 2

∴ f(n) = 2n - 3  ..........is the required function

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Step-by-step explanation:

20:16

Reduce the ratio to lowest terms by dividing both numbers by 4.

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Find the sum of 10 + 5i and its complex conjugate.<br> Write your answer in the form a + bi
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Graph the equation F(x)=(1/3)^x
scoray [572]

The value of a=9,b=3 and c=1

Step-by-step explanation:

The graph shown is for function f(x)

The given function is f(x)=(\frac{1}{3}) ^{x}

Table says,

X      Y

-2      a

1        b

0       c

1     (1/3)

2    (1/9)

To find value of a:

From table, for output value a, input value, x=(-2)

we can write f(-2)=a

Therefore,

f(x)=(\frac{1}{3}) ^{x}

f(-2)=(\frac{1}{3}) ^{(-2)}

a=(\frac{1}{3^{(-2)}})

a=3^{(2)}

a=9

To find value of b:

From table, for output value a, input value, x=(-1)

we can write f(-1)=b

Therefore,

f(x)=(\frac{1}{3}) ^{x}

f(-1)=(\frac{1}{3}) ^{(-1)}

b=(\frac{1}{3^{(-1)}})

b=3^{(1)}

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To find value of c:

From table, for output value a, input value, x=(0)

we can write f(0)=c

Therefore,

f(x)=(\frac{1}{3}) ^{x}

f(0)=(\frac{1}{3}) ^{(0)}

c=(\frac{1}{3^{(0)}})

c=1

5 0
3 years ago
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