Arithmetic Sequences
What is the formula for an Arithmetic Sequence?
an = a1 + (n - 1)d
What is the formula for an Arithmetic Series
Sn=(n/2)(a1+an)
What is the formula for a geometric series? What are the first four terms of the following sequence? an=3*(-1/3)n-1
an = a1(r)n-1
3, -1, (1/3), (-1/9)
What is the formula for the sum of a geometric series.
Must have both partial and infinite sum.
Sn=(a1(1-rn))/(1-r)
S=a1/(1-r)
|r|<1
Rewrite using sigma notation: 1 + 4 + 9 + 16 + 25
m=1 to 5
E (m2)
Write an explicit formula for the following sequence:
-24, -20, -16, ...
an=4n-28
Find the sum of the following sequence: 1,2,3,4,5,6....111,112,113,114
6555
Write a recursive formula for the following sequence: 8, -4, 2, -1, ...
a1=8
an=(-1/2)*an-1
Find the sum of the following sequence: 3, 12, 48, ... , 196608
262,143
Rewrite using sigma notation: 1 + 1/2 + 1/3 + 1/4 + 1/5
n = 1 to 5
E (1/n)
How many terms are in the following sequence? 1,3,5,7...43
22 terms
Find S98 for the following series:
0.2, 0.4, 0.6, ...
970.2
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 :-)
Rewrite using sigma notation: 1/3 + 1/9 + 1/27 + 1/81 + 1/243 + 1/729
n = 1 to 6
E (1/3n)
What are the first four terms of the following sequence?
a1=12
an=an-1 - 23
12, -11, -34, -57
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
What is the equation to find the 89th term of this sequence?
3, 15, 75, 375
3*5(89-1)
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 sales for the company in the 8th month?
$30590.23
Rewrite using sigma notation: 5 + 25 + 125 + 625 + 3125
n = 1 to 5
E (5n)
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
Find the sum of this series
8.9,17.8,26.7,35.6,44.5 ... 1619.8
148211.7
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
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
Rewrite using sigma notation: 1/2 + 2/3 + 3/4 + 4/5 + 5/6
n = 1 to 5
E (n/(n+1))