This right over here is a sub 4. So this is clearly an arithmetic sequence.
For the second term, we added 4 once. We'd call it a sub 2. The answer lies in the concept of mathematical proof. But I could use the notation b sub k or anything else.
The method described here will not work for sequences like this one that are not polynomial sequences.
So just to be clear, this is one definition where we write it like this, or we could write a sub n, from n equals 1 to infinity.
But I want to make us comfortable with how we can denote sequences and also how we can define them. Starting at k, the first term, going to infinity with-- our first term, a sub 1, is going to be 3, now.
Nobody, not even an experienced mathematician, writes a complete, well-written proof from start to finish the first time they try.
There are some conjectures in math that have eluded all attempts at proof for hundreds of years. So a given term is equal to the previous term.
That's how much you're adding by each time. When k is 3, we get 7.