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Arithmetic Sequences & Series

100

State the common difference for the sequence:

3, 7, 11, 15, ...

4

200

Write an explicit equation for the arithmetic sequence:

2, 11, 20, 29, ...

a_n=2 + 9(n-1) = 9n-7

300

Find the sum of the series: 

10+20+30+40+...+200

2100

400

Find the 9th term for the arithmetic sequence where the 5th term is -2 and the 13th term is 30.

14

Geometric Sequences & Series

100

State the common ratio for the sequence:

60, 30, 15, 7.5, ...

r=1/2

200

Write the expression to find a₂₀ for the sequence:

1, 1/2, 1/4, 1/8

a₂₀=(1/2)^19

300

Write the following series in sigma notation:

3+12+48+192+...+49152

Sum of 3*4^(i-1) from i=1 to i=8

400

Determine if the series converges or diverges. If it converges. Find its exact value:

Sum from k=1 to infinity of 9(-1/2)^k

Converges. 

-3

Sigma Notation

100

Write out the terms for the series:

sum from i=1 to i=4 of (9-i). Find the sum. 

8+7+6+5=26 

200

Write the terms and determine the sum for:

Sum from i=-2 to i=10 of 5. 

5+5+5+5+5+5+5+5+5+5+5+5+5=65 

300

Write the series below in sigma notation: 

1/2+2/3+3/4+5/6+...+13/14

Sum from i=1 to i=13 of i/(i+1)

400

Write out the terms and determine the sum for:

Sum from i=0 to i=3 of ((-1)^i)(2^(i+1))

2-4+8-16=-10 

Real-World Applications

100

You are hired at an annual salary of $58,000 and expect an annual increase of 5%. What will your salary be in your sixth year? 

$74,024.11

200

A brick staircase has 30 steps. The bottom step requires 100 bricks, and each successive step requires two fewer bricks. How many bricks are required for the top step? 

42

300

Using the staircase from the previous problem, how many total bricks are required to build the entire staircase?

2130

400

A commoner asks for wheat on a 64-square chessboard: 1 grain on the first square, 2 on the second, 4 on the third, and so on. Compute the formula for the total number of grains needed to fill the board. 

S₆₂=(2^64)-1

Spicy Problems

100

Find x so that x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence.

3/2

200

• For the sequence an=3n/2, what is the exact value of the common ratio? 

  +1

  
  

• 
  

sqrt 3

300

Algebraically determine the value of n such that 

from k=1 to k=8 of Σ(8k−3)=8145. 

n=45

400

If a_n=5^n and b_n=log(a_n), evaluate and fully simplify:

the sum from n=1 to 8 of b_n

36log5 

or

log (5^36)