TOPIC 1 ALGEBRA ARITHMETIC SEQUENCES & SERIES S. Aldous, A.
Beetz & S. Thauvette IB DP SL Mathematics
Slide 2
You Should Be Able To State whether a sequence is arithmetic,
giving an appropriate reason Find the common difference in an
arithmetic sequence Find the nth term of an arithmetic sequence
Find the number of terms in an arithmetic sequence Solve real-world
problems involving arithmetic sequences and series.
Slide 3
Challenge Nobs Tricky Sequence Nob Yoshigahara discovered this
beautiful number sequence. Can you work out the logic behind the
sequence and fill in the missing number?
Slide 4
Make some sequences by picking four numbers that form a
pattern. Record as many as you can.
Slide 5
How do you see this pattern growing? Draw shapes 4 and 5. How
many matchsticks are in shape 10? Can you describe the pattern
using algebra?
Slide 6
Finding the General Term Use 2 pieces of paper. On one, make up
a value for u 1. On the other, make up a value for u 4. Swap the
cards with someone else. Find the general term for the arithmetic
sequence. Make sure you both agree.
Slide 7
Each day a runner trains for a 10km race. On the first day she
runs 1,000m, and then increases the distance by 250m each
subsequent day. On which day does she run a distance of 10km in
training?
Slide 8
In an arithmetic sequence, the first term is 2, the fourth term
is 16, and the nth term is 11,998. Find the common difference d.
Find the value of n
Slide 9
Question Finding U n Given Two Terms In an arithmetic sequence,
U 7 = 121 and U 15 = 193. Find the first three terms of the
sequence and U n. Substitute know values in the formula for the nth
term to write a system of equations. Then, solve the system. Since
a = 67 and d = 9, the first three terms of the sequence are 67, 76,
and 85.
Slide 10
Finding U n Given Two Terms continued To find U n, substitute
67 for a and 9 for d in the formula for the nth term. U n = 67 + (n
1)9 U n = 67 + 9n 9 U n = 9n + 58 Thus, the first three terms are
67, 76, and 85, and U n = 9n + 58.
Slide 11
You Should Know A sequence is arithmetic if the difference
between consecutive terms is the same An arithmetic sequence has
the form: u 1, u 1 + d, u 1 + 2d, u 1 + 3d, , u 1 + (n 1)d The
common difference can be found by subtracting a term from the
subsequent term: d = u n + 1 u n When to use the term formula
Slide 12
You should know: Textbook: Arithmetic Sequences p.155 159
Homework: Arithmetic SequencesArithmetic Sequences
Slide 13
ARITHMETIC SERIES S. Aldous, A. Beetz & S. Thauvette IB DP
SL Mathematics
Slide 14
Arithmetic Series Calculate the sum of the first n terms of an
arithmetic series
Slide 15
Challenge The top three layers of boxes in a store display are
arranged as shown. If the pattern continues, and there are 12
layers in the display, what is the total number of boxes in the
display?
Slide 16
Treasure Hunt In the pod there are ten pink cards. Find any
card. Note down its number. Solve the question on the card. Find
the answer on another card somewhere in the pod. Note down the
cards number. Continue answering questions and noting the card
numbers. You should finish at the same card you started. Show your
teacher the list of card numbers you visited.
Slide 17
Sum of a Series Given First Terms Find the sum of the first 60
terms of the series: (a) 5 + 8 + 11 +
Slide 18
Sum of a Series Given First and Last Terms Consider the series
17, 7, 3, , 303. (a) Show that the series is arithmetic. Show that
the difference between two consecutive terms is constant. For
example: 7 17 = 3 7 = 10 Therefore, d = 10 and the series is
arithmetic
Slide 19
Continued Consider the series 17, 7, 3, , 303. (b) Find the sum
of the series. The formula for the sum of an arithmetic series
requires the value of n. Use the term formula first to find n. n =
33 Now use the appropriate formula to find the sum of the first 33
terms. S 33 = 4719
Slide 20
Question The sum of the first five terms of an arithmetic
series is 65/2. Also, five times the 7 th term is the same as six
times the second term. Find the first term and common
difference.
Slide 21
Question continued
Slide 22
Be Prepared Look for words or expressions that suggest the use
of the term formulaafter the 10 th month, in the 8 th rowand those
that suggest the sum formula total cost, total distance,
altogether. Look for questions in which information is given about
two terms. This normally suggests the formation of a pair of
simultaneous equations that you will have to solve to find the
first term and the common difference. The last term of a sequence
can be used to find the number of terms in the sequence
Slide 23
You should know: When to use the sum formula Textbook:
Arithmetic Series p.167 169 Homework: Arithmetic SeriesArithmetic
Series
