2(3w-2+w)
=2(4w-2)
=8w-4

the formula for solving perimeters is 2(WL). so L=3w-2, because the question said the length is 2 units shorter than 3 times the width, and the width is w. so the final equation is 2(3w-2+w), and then you just have to simplify that

8 0

3 years ago

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

riadik2000 [5.3K]

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

7 0

3 years ago