Download 12.2 Arithmetic Sequences

Precalculus 12.2 Arithmetic Sequences
Objective: able to determine if a sequence is arithmetic; find a formula for an arithmetic sequence; find the sum of an
arithmetic sequence (an arithmetic series).
A sequence is called an arithmetic sequence when the difference between any two successive terms is
always the same number. Thus, an arithmetic sequence may be defined recursively as
a1 = a, a n − a n −1 = d , or as a1 = a, a n = a n−1 + d where a1 = a and
number a is the first term, and the number d is the common difference.
The terms of an arithmetic sequence with first term
a, a + d , a + 2d , a + 3d ,…
d
are real numbers. The
a and common difference d follows the pattern:
1. Show that the sequence {3n + 1} is arithmetic. Find the first term and the common difference.
a is the first term of an arithmetic sequence whose common difference is d.
a
formula for the nth term, n .
Suppose that
For an arithmetic sequence
determined by the formula:
Let’s find a
{a n } whose first term is a and whose common difference is d, the n
th
term is
2. Find the 80th term of the arithmetic sequence -1, 1, 3, ….
3. Find the first term and the common difference of the arithmetic sequence with 4th term3 and 20th term
35. Give the recursive formula for this sequence.
Develop a formula for the sum of the first
For an arithmetic sequence
first
n terms of an arithmetic sequence.
{a n } whose first term is a and whose common difference is d, the sum Sn
n terms is determined by the formula:
of the
4. Find the sum of 2 + 4 + 6 + …+ 2n.
5. Find the sum of 2 + 5 + 8 + …+ 41.
6. Find the sum of the first 25 terms of the sequence {2.67n – 1.23}.
7. A brick staircase has a total of 30 steps. The bottom step requires 100 bricks. Each successive step
requires two less bricks than the previous.
a. How many bricks are required for the top step?
b. How many bricks are required to build the staircase?
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