12-1 Arithmetic Sequences and Series

Sequence- A function whose domain is a set of natural numbers

Arithmetic sequences: a sequences in which the terms vary by a common difference

Notation: a1, a1 + d, a1 + 2d, a1 +3d….

Practice:

1) Find the next four terms in the sequences:

-5, -2, 1,…

Recursive formula: a formula that requires computations of the previous terms, to find the current term.

If you don’t want to find all the previous numbers, you can use the

formula

An = a1 + (n-1)d

Practice:

2) Find the 47th term in the sequence -4, -1, 2, 5….

3) Find the first term in the arithmetic sequence for which a19 = 42 and d= -2/3

4) Write an arithmetic sequence that has five terms between 4.9 and 2.5

Arithmetic series – the SUM (+) of an arithmetic sequences

Example: Sequence: 3,5,7Series: 3+ 5+ 7

nth Partial Sum (Sn): The sum of the first n terms

Sn =

5) Find the sum of the first 60 terms in the series 9 + 14 + 19+….+ 304