Enter Title

Patterns and Recognition

100

What is the pattern in this sequence?

5, 1, 1/5, 1/25, …

divide by 5

200

The pattern of a sequence is “multiply by 2 and then add 3”. If the first term of this sequence is -4, what are the next two terms?

-5 and -7

300

Is this sequence arithmetic? geometric? or neither?

4, -2, -14, -38, …

neither

400

Find the common ratio.

-2/3, -5/6, -25/24, …

5/4

500

Find the common difference of the arithmetic sequence with a₁=-16 and a₂₉=20.

9/7

Arithmetic Sequence and Series

100

Find a₅₀ of this arithmetic sequence:

-24, -20, -16, …

172

200

Write the explicit formula for this sequence:

-24, -20, -16, …

a_n=4n-28

300

How many terms are in this sequence?

1, 3, 5, 7,…, 43

22 or 22 terms

400

Cans are stacked in a display of rows with 1 can in the top row, 4 cans in the second row, 7 cans in the third row and so on. If there are 298 cans in the bottom row, how many cans total are there in the display?

14,950 cans

500

Find the sum of this series:

8.9+17.8+26.7+35.6+44.5+…+1619.8

148,211.7

Geometric Sequences and Series

100

Find the 11th term of the following sequence:

3, 15, 75, 375, …

29,296,875

200

Write the recursive formula for the following sequence: 8, -4, 2, -1, ...

a_n=a_n-1 (-1/2)

300

What term is -625,000 in the following sequence? 

-8, -40, -200, -1000, … , -625000

8th or 8th term

400

Find the sum of the first 10 terms of the following sequence:

3, 15, 75, …

7,324,218

500

Frank just bought a new car for $16,000. At the end of the year, the car's price was $14,720 and at the end of the 2nd year, the price was $13,542.4. If the car's price continues depreciating every end of the year in this pattern, how much will the car be worth at the end of 10 years? (Hint: Find a₁₁.)

$6,950.22

Arithmetic Sigma

100

Find the first three terms of this arithmetic series:

    20

Sigma 3n 

   n=1

3, 6 and 9

200

Write this arithmetic series into sigma notation:

8+10+12+…+198

   96

Sigma 2n+6

   n=1

300

Write this sigma notation of arithmetic series into standard form.

   100

Sigma -5n+10

   n=1

5+0+(-5)+…+(-490)

400

Find the sum.

    35

Sigma 3n-13

   n=1

1,435

500

Find the sum.

  45

Sigma 3n-9

  n=1

2,700

Geometric Sigma

100

Find the first three terms of this geometric series. 

    20

Sigma 4^n-1

    n=1

1, 4 and 16

200

Write this geometric series into a sigma notation.

7+14+28+…+896

   8

Sigma 7(2)^n-1

  n=1

300

Write this sigma notation of geometric series into its standard form.

    15

Sigma 3(-2)^n-1

   n=1

3+(-6)+12+…+49152

400

Find the sum.

    9

Sigma 5(2)^n-1

  n=1

2,555

500

Find the sum.

 3+12+48+…+12,288

  

16,383