Respuesta :
First, determine what type of sequence the set of numbers make up. Through simple logic, it is an arithmetic sequence, because one can see by inspection that there is a common difference of 3 (positive 3, just to be a bit more pedantic).
We then use the formula, [tex] t_{n} = a + (n - 1)d[/tex]
where [tex] t_{n} [/tex] represents the [tex] n^{th} [/tex] term; a represents the starting term (so the first number in the set of numbers, which in this case is -6); n is the term number (1st, 2nd, 3rd term, etc.); d is the common difference, that is, when you subtract the next term to the previous term – what is that numerical value.
To elaborate a bit more, your 1st term is -6, 2nd is -3, 3rd is 0, etc.
Also, the formula above is something you just learn, unless you learn to proof this formula, which is something different.
So, here, [tex] t_{n} = -6 + (n-1)3[/tex], which can be expanded to:
[tex] t_{n} = -6 + 3n-3[/tex]
Therefore, [tex] t_{n} = 3n - 9[/tex]
We then use the formula, [tex] t_{n} = a + (n - 1)d[/tex]
where [tex] t_{n} [/tex] represents the [tex] n^{th} [/tex] term; a represents the starting term (so the first number in the set of numbers, which in this case is -6); n is the term number (1st, 2nd, 3rd term, etc.); d is the common difference, that is, when you subtract the next term to the previous term – what is that numerical value.
To elaborate a bit more, your 1st term is -6, 2nd is -3, 3rd is 0, etc.
Also, the formula above is something you just learn, unless you learn to proof this formula, which is something different.
So, here, [tex] t_{n} = -6 + (n-1)3[/tex], which can be expanded to:
[tex] t_{n} = -6 + 3n-3[/tex]
Therefore, [tex] t_{n} = 3n - 9[/tex]
Answer:
3n-9
Step-by-step explanation:
NO NEED TO EXPLAIN ENJOY :)
