Ok, I haven't done as much with sequences, but I'll try to explain it.
First, in sequences, you can write the value of each term as a function of n (the term you are on). There are many different types of sequences, but if it says the difference between terms is constant that means it is arithmetic(i think)
basically this means in the equation that describes the sequence, there won't be any powers to juggle.
In arithmetic sequences, you have a coefficient, n, and a constant. so it is ?n + or - ?
The coefficient of n is the difference between terms, so that is the best place to start.
You are given two terms, and their values. The difference between 4 and 11 (your terms) is 7. The difference between 47 and 19 (your values) is 28. To find the difference per term, divide 28 by 7 to get 4. (Think about slope of a line - it's the same idea)
now you have 4n + ?. You are given a term and its value, so you can use substitution. When n is 4, your value is 19.
so 4(4) + ? =19
16+?=19
?=3
Now you can write your equation
value=4n+3
finally substitute 1 for n
value=4(1)+3
value=7
answer c
If you look at the process, it is just like finding the equation of a line given two points.
The difference between values is just like how much y increases when x increases by 1 (slope) the value you add is just like the y intercept, it shifts your starting value by its value.
Series can get much more complex than this, but for arithmetic series (I'm pretty sure that's the name for it) it is a lot like finding the equation of a line.
Replies to: I need help with the following Math questions!!
First, in sequences, you can write the value of each term as a function of n (the term you are on). There are many different types of sequences, but if it says the difference between terms is constant that means it is arithmetic(i think)
basically this means in the equation that describes the sequence, there won't be any powers to juggle.
In arithmetic sequences, you have a coefficient, n, and a constant. so it is ?n + or - ?
The coefficient of n is the difference between terms, so that is the best place to start.
You are given two terms, and their values. The difference between 4 and 11 (your terms) is 7. The difference between 47 and 19 (your values) is 28. To find the difference per term, divide 28 by 7 to get 4. (Think about slope of a line - it's the same idea)
now you have 4n + ?. You are given a term and its value, so you can use substitution. When n is 4, your value is 19.
so 4(4) + ? =19
16+?=19
?=3
Now you can write your equation
value=4n+3
finally substitute 1 for n
value=4(1)+3
value=7
answer c
If you look at the process, it is just like finding the equation of a line given two points.
The difference between values is just like how much y increases when x increases by 1 (slope) the value you add is just like the y intercept, it shifts your starting value by its value.
Series can get much more complex than this, but for arithmetic series (I'm pretty sure that's the name for it) it is a lot like finding the equation of a line.