<p>Ok, I haven’t done as much with sequences, but I’ll try to explain it.</p>
<p>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)</p>
<p>basically this means in the equation that describes the sequence, there won’t be any powers to juggle.</p>
<p>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.</p>
<p>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)</p>
<p>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</p>
<p>Now you can write your equation
value=4n+3</p>
<p>finally substitute 1 for n
value=4(1)+3
value=7</p>
<p>answer c</p>
<p>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.</p>
<p>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.</p>