Sequences and Series Test:
TEST TOPICS (test is on Friday 4/9)
I.Arithmetic Sequences and Series- formulasfor nth term, and 2 formulas for sum of n terms
1) determine whether a sequence is arithmetic.
2) Find missing values: a1, d, n, an
3) Word problems involving arithmetic sequences and sums
4) Arithmetic mean between 2 numbers
5) word problems- determine a1, d, n, an , Sn
6) sum of all terms divisible by a given number
II.Geometric Sequences and series- know formula for the nth term, and sum of n terms
1) finding missing values, : a1, r, n, an
2) geometric mean between 2 numbers
3) word problems- understand which exponent to use in various problems such as 91-98 on SS Sheet
4) find missing values
5) Applications including distance traveled by a pendulum- determine length of the nth arc, and total distance
travelled after a given number of swings
III. Infinite Geometric Series
1) Infinite geometric sequences and series
Find S when [pic]
2) Applications of infinite geometric series including:
a. distance traveled for pendulum to come to rest
b. distance traveled for bouncing ball to come to rest
3) Convert repeating decimals to fractions using sums of infinite geometric series
4 ) Infinite sequences (including sequences other than arithmetic and geometric also)
5) Determine whether an infinite sequence converges or diverges – if it converges, find the limit
6 )Sigma notation – evaluating, including sums of arithmetic and geometric series
7) Writing an expression for the nth term of a sequence, and writing a series in sigma notation
III. Fractals – know the following:
1 ) what a fractal is, and what are some of its properties
2) how to generate the Menger Sponge and how to generate a formula for the number of squares at
stage n and the area of the unshaded squares at stage n
3) how to generate the Sierpinski triangle and how to generate a formula for the area of the unshaded
triangles at stage n
VACATION ASSIGNMENT:
Review Homework due Wednesday: (to count as a triple assignment)
Do all problems neatly and carefully on looseleaf. Show work!
I.) SS Sheet I: 20, 42f, 53,68h,i,79,86,92, 93, 9,103,105d, 107 ,110n,o, 125
II.) Find the sum of all the integers between 200 and 500 that are divisible by 6.
III. Write a formula for an:
1. 8, 5, 2, –1, –4,…
2. 1, –4, 9, –16, 25,…
3. [pic]
IV. State the limit of the sequence if it exists. Otherwise, state “diverges”:
4. [pic]
5. [pic]
6. 1000, –500, 250, –125,…
V. Write in sigma notation:
7. 2 – 4 + 8 – 16 + … + 128
8. 2 – 5 + 8 – 11 + 14 – 17 + … – 35
VI. Evaluate, if possible:
9. [pic]
10. [pic]
11. [pic]
12. [pic]
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