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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