11.2 Arithmetic Sequences
Warm up:
1.) Find the equation of a line in slope intercept form that passes through (8, 50) and
slope is ¼.
2.) Find the equation of a line in slope intercept from that passes through the two
points (6, 10) and (21, 55)
Arithmetic
Arithmetic SSequence
equence: a sequence where the difference between consecutive terms is
constant, denoted by d.
Ex: Decide whether each sequence is arithmetic.
a) −3, 1, 5, 9, 13, …
b) 2, 5, 10, 17, 26, …
c) −10, −6, −2, 0, 2, 6, 10, …
d) 5, 11, 17, 23, 29, …
e) 1, 1, 2, 3, 5, 8, …
f) 32, 16, 8, 4, …
Ex: Write a rule for the nth term of the sequence −2, 1, 4, 7, …. Then find a20.
(Graph then make an x/y chart to help see a pattern…what do you notice?)
Rule for an Arithmetic sequence: the nth term of an arithmetic sequence can be
determined using the formula below…
an = dx + b
Ex:
Ex: Write a rule for the nth term of the sequence.
a) 50, 44, 38, 32, …. Then find a18
b) 32, 47, 62, 77, …. Then find a12
c) 17, 11, 5, −1, −7, …. Then find a15
Ex:
Ex: Finding the nth term given a term and the common difference (Hint: Think of
finding an equation using the slope and a given point.)
a) One term of an arithmetic sequence is a13 = 30. The common difference
is d =
3
.
2
b) One term of an arithmetic sequence is a8 = 50. The common difference is
d = 0.25 .
c) One term of an arithmetic sequence is a20 = −111. The common difference
is d = −6 .
d) One term of an arithmetic sequence is a2 = 18. The common difference is
d = 18 .
Ex:
Ex: Finding the nth term given two terms. (Hint: Think about how to find the
equation of a line given two points.)
a) Two terms on an arithmetic sequence are a6 = 10 and a21 = 55. Then find
n when an = 40.
b) Two terms on an arithmetic sequence are a5 = 10 and a30 = 110. Then
find n when an = −2.
c) Two terms on an arithmetic sequence are a8 = 12.5 and a15 = 30. Then
find n when an = 50