Sequences and equations:

position = 10, 11, 12, 13, 14
value of term = 28, 31, 34, 37

Sequences
Sequence: a function whose domain is a set of consecutive integers.
Domain: the position of the term (1st, 2nd, 3rd, and so on).
Range: the terms of the sequence.
Terms: the numbers in the sequence.
Finite Sequence: a sequence that has a last term.
Infinite Sequence: a sequence that continues without stopping.
Rule for the nth term: means to write an equation of the arithmetic sequence.
Look at the following sequences:
an = 2, 4, 6, 8 an = 2, 4, 6, 8, …..
If n represents the position of the term, then a2 refers to the 2nd term.
Writing Terms of Sequences
To write the first six terms of a sequence, plug the numbers 1 – 6 in for n.
Example 1: Write the first six terms of the sequence.
a) an = 5 – n b) f(n) = 5n
Example 2: Write the next term in the sequence.
a) 1, 4, 9, 16, 25, , … b) 5, 25, 125, , … c) 456 , , , ,...
789
d) 0, 3, 8, 15, 24, , … e) 1, 2, 5, 10, 17, , …