Sequences and Series Week 1

Writing Rules for Arithmetic Sequences

100

Write a rule for the n^th term of the arithmetic sequence.

a_1=13, d=-2

a_n=15-2n

200

Write a rule for the sequence. Then, find a_20.

{-7, -4, -1, 2, ...}

a_n=3n-10 ;a_20=50

300

Write a rule for the n^th term of the arithmetic sequence. 

a_23=107;d=4

a_n=4n+15

400

Write a rule for the n^th term of the arithmetic sequence.

a_1=-27;a_18=41

a_n=4n-31

500

Write a rule for the n^th term of the arithmetic sequence.

a_15=28;a_24=34

a_n=2/3n+18

Non-Arithmetic Sequences

100

Give the first 5 terms of the sequence

a_n=n^3-20

-19, -12, 7, 44, 105

200

Write an explicit formula to represent the sequence, then find a_12.

{8,11,16,23,32,...}

a_n=n^2+7;a_12=151

300

Write a recursive formula to represent the sequence, then find a_7.

{4,11,32,95,284,...}

a_1=4;a_n=3a_(n-1)-1

a_7=2,552

400

Write a recursive formula to represent the sequence.

{1/2,1,7/4,61/16,...}

a_1=1/2;a_n=(a_(n-1))^2+3/4

500

Write an explicit formula to represent the sequence.

{-4,8,-12,16,...}

a_n=(-1)^n4n

Recursive Sequences

100

Give the first 5 terms of the sequence

a_1=3,a_2=8;a_n=2a_(n-2)+a_(n-1)

3, 8, 14, 30, 58

200

Write an explicit rule for

a_1=-5;a_n=a_(n-1)-2

a_n=-3-2n

300

Write a recursive rule for 

a_n=-6+8n

a_1=2;a_n=a_(n-1)+8

400

Write a possible recursive rule, then find a₆.

{1,3,7,17,...}

a_1=1, a_2=3;a_n=a_(n-2)+2a_(n-1)

a_6=99

500

Write a possible recursive rule for the sequence.

{120,68,42,29,22.5,...}

a_1=120;a_n=1/2a_(n-1)+8

Evaluating Series

100

Find S₂₇ of the series.

{(-2)+(-7)+(-12)+(-17)+...}

-1,809

200

Expand and evaluate the series.

sum_(n=1)^10(n-2)^2

205

300

sum_(k=1)^31 7k-3

3,379

400

sum_(x=5)^23 1-2x

-513

500

Find S_30.

a_1=2;a_n=a_(n-1)-2

-810

Famous Mathematicians

100

Which ancient Greek mathematician is the following theorem named after?

For any right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Pythagoras

200

Which Italian mathematician from the middle ages is the following sequence of numbers named after?

{0, 1, 1, 2, 3, 5, 8, 13, 21,...}

Fibbonacci

300

Which ancient Greek mathematician derived and proved the formula for area of a circle?

Archimedes

400

Which ancient Greek mathematician, known for writing the Elements, is considered the "father of geometry?"

Euclid

500

Pronounce this last name: Euler

Pronounced like "oiler"