A geometric sequence has a1 = 1 and r = 2. Find the first four terms of the sequence.
To get the next term, we multiply the term we're on by r = 2.
a2 = a1(2) = 2
a3 = a2(2) = 4
a4 = a3(2) = 8.
This isn't a very useful form for seeing patterns. However, if we write each term as its prime factorization, then we can see what's going on.
From this table, we can conclude that the nth term is
an = 2n – 1.
Multiplying numbers together hides patterns. Since we like patterns so much, we are going to keep expressions in factored form. It'll be easier to see what's going on.