Sequences & Series Review

Arithmetic Sequences

100

What is the formula for an Arithmetic Sequence?

t_n = t₁ + (n - 1)d

200

Write the general term for the following sequence:

-24, -20, -16, ...

t_n=4n-28

300

How many terms are in the following sequence? 1,3,5,7...43

21 terms

400

What are the first four terms of the following sequence?

t₁=12

t_n=t₁+(n-1)(-23)

12, -11, -34, -57

500

Cans are stacked in a display of 25 rows with 1 can in the top row, 3 cans in the second row, 5 cans in the third row and so on. How many cans are in the 12th row?

23 cans

Arithmetic Series

100

What is the forumla for an Arithmetic Series

S_n=(n/2)(t₁+t_n) OR S_n=(n/2)(2t₁+(n-1)d)

200

Find the sum of the following sequence: 1,2,3,4,5,6....111,112,113,114

6555

300

Find S₉₈ for the following series:
0.2, 0.4, 0.6, ...

970.2

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 n and find the sum of this series

8.9,17.8,26.7,35.6,44.5 ... 1619.8

n=182

S_n=(182/2)(8.9+1619.8)

Geometric Sequences

100

What is the formula for a geometric series? What are the first four terms of the following sequence? t_n=3*(-1/3)^n-1

t_n = t₁(r^n-1)

3, -1, (1/3), (-1/9)

200

Write the general term for the following sequence: 8, -4, 2, -1, ...

t_n=8(-1/2)^n-1

300

What is the 17th term of the following sequence? 65, 45.5, 31.85, 22.295, ...

0.22

400

What is the equation to find the 89^th term of this sequence?

3, 15, 75, 375

3*5^89-1

500

Eddie just bought a new car for $16,000. If the car depreciates at 8% per year how much will the car be worth at the end of 10 years?

$6,950.22

Geometric Series

100

What is the formula for the sum of a geometric series.

S_n=(t₁(1-rⁿ))/(1-r) OR S_n=(r(t_n)-t₁)/(r-1)

200

Find the sum of the following sequence: 3, 12, 48, ... , 196608

262,143

300

Susan started a new running program... on May 1st she ran 0.2 miles. Her plan each day is to double the amount she ran the day before. How many total miles will she run during the month of May? Is this really a possible training regimen??

429,496,729.4 miles - no way this is possible :-)

400

A new shoe company sold $10,000 worth of product in their first month. They believe they will increase sales by 15% each month over their first year. If this increase does occur what will be the total sales for the company in their first year?

$290,016.67

500

You decide to save money for a car. On the first day you deposit $500 into an account. Every two weeks you deposit 5% more than you did the previous time. How much money will you have in the account after 112 days?

$4774.55

Infinite Series

100

What is the general term for an infinite series?

S_inf=t₁/(1-r), -1<r<1

200

Is this series convergent or divergent? -3+ 1+(-1/3)+... If it is convergent, what is its sum?

Convergent and has a sum of -2.25

300

The sum of an infinite series is 50 and its common ratio is 4/5. What is the first term?

10

400

The sum of an infinite series is 3 times the first term. Determine the common ratio

r=2/3

500

A ball is dropped from a height of 50m. Each time it bounces it rises to 50% of its previous height. If the ball continues to bounce until it stops, what is the total vertical distance travelled?

150m