Section 11.2 ­­ Arithmetic Sequences
An arithmetic sequence is a sequence where the difference
between consecutive terms is a constant.
a, a + d, a + 2d, a + 3d, a + 4d, ...
d = common difference
Example: Are the following sequences arithmetic? If yes,
what is the common difference.
2, 5, 8, 11, ...
3, 4, 6, 9, 13, ...
Finding the nth term of an arithmetic sequence
2, 5, 8, 11, ..., n, ...
Formula for the nth term of an arithmetic sequence:
the nth term of an arithmetic sequence is given by:
Examples:
Find the formula for the nth term of the arithmetic sequence with a1 = 4 and d = ­2. Then find the 100th term.
If a3 = 9 and a7 = 21, find the formula for the nth term of the arithmetic sequence.
Partial Sums of an Arithmetic Sequence
pg. 835
Formula for the nth partial sum of an arithmetic sequence:
the nth partial sum of an arithmetic sequence is given by
or
Examples: Find the sum of the first n terms of the arithmetic sequence defined below.
a1 = 4, d = 5, n = 12
a1 = ­3, d = ­2, n = 7
Find the seating capacity of an auditorium that has 25 rows if row 1 has 25 seats, row 2 has 27 seats, row 3 has 29 seats, etc.