How do you express the numbers 3, 7, 11... as a linear function using a linear equation?

I just saw this problem and the answers but still don't understand it. Please give an understandable explaination(accurate, please!). Thanks in advance!How do you express the numbers 3, 7, 11... as a linear function using a linear equation?
sometimes one method of showing how it works doesn't make sense to everyone. Here's how I would explain it.





think of y = mx + b


where m = the increment (difference) between numbers


so y = 4x + b


now enter the first number of the sequence


3 = 4x + b


What is x? It's the spot in the sequence of number. Since 3 is the first number x=1


3 = 4 + b


What does b equal? 3 - 4 = -1


y = 4x + b becomes


y = 4x - 1How do you express the numbers 3, 7, 11... as a linear function using a linear equation?
The set can be represented as A={x | x=4*i+3 for i in Z+, the set of positive integers}.





So this can be written as f(i)=4*i+3 starting for i in {0,1,2,.....}.
look. the succeeding number is just 4 more than its preceding one





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


where x is the xth term of your sequence





this could be simplified as


f(x)=4x-4+3


f(x)=4x-1
It's going up in fours so it is 4n. If it was going up in threes it would be 3n.


And if you go back a number you would have -1 so it is 4n-1





eg,...6, 16, 26, ....





going up in 10's so 10n and if you go back a number in the sequrence you get -4 so it is 10n-4
A linear equation is an expression where the highest degree term in the variable or variables is of first degree.





Linear eqn may consist of one , two or more variables.





so if I use one variable it can be


3a +7a = 11


or 3a +7 = 11


or 3a -7 = 11





Using two variables





3a + 7b = 11
7-3=11-7=....=4 --%26gt; f(x)=4x-1 because f(1)=3





saludos.

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