TABLE OF CONTENTS
Find a formula for the general term of the sequence
1, 2, 3, 4,...
if the sequence starts at
(a) n = 1
(b) n = 0
(c) n = 194
(a) This is the easy one. The formula is an = n.
(b) Make a table so we can see the relationship between n and the term. This time, the table starts with n = 0 instead of n = 1.
The formula for the general term if we start at n = 0 is an = n + 1.
(c) Let's make a table so we can see the relationship. Start the table off at n = 194.
If we start this sequence at n = 194, the nth term is an = n – 193.
If we look at the denominators first we see the sequence
It makes sense to start this sequence at n = 1. In order for the first term to be positive and the terms to alternate sign, we must multiply by (-1)n + 1.
The general term of the sequence, starting at n = 1, is
If we look at the signs first we see
This can be described by (-1)n, starting at n = 0. Then the denominator of the nth term is (n + 1). The general term, starting at n = 0, is