Arithmetic Sequences
What is the formula for an Arithmetic Series?
s_n=n((a_1+a_n)/2)
What are the first four terms of the following sequence?
a_n=3*(-1/3)^(n-1)
3, -1, 1/3, -1/9
What is the formula for the sum of a finite geometric series.
S_n=a_1((1-r^n)/(1-r))
What is the formula for an infinite geometric series?
S=a_1/(1-r), abs(r)>1
Write an explicit formula for the following sequence:
-24, -20, -16, ...
a_n=4n-28 or a_n=-24+(n-1)*4
Find the sum of the following sequence: 1,2,3,4,5,6....111,112,113,114
6555
Write a formula for the following sequence: 8, -4, 2, -1, ...
a_n=8(-1/2)^(n-1)
Find the sum of the first 10 terms of following sequence: 3, 12, 48, ...
1,048,575
Can you find the series of the following? Why or why not? If so, find it. 3 - 6 +12 - 24 + ...
No, r=-2 which means that
abs(r)>1
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 realistic training regimen??
429,496,729.4 miles - no way this is possible :-)
Find the infinite geometric sum of 9 + 3 + 1/3 + ...
S=13.5
What are the first four terms of the following sequence?
a_n=12
d = -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 total sales for the company in their first year?
$290,016.67
Find the common ratio given
a_1=8
and S=20
r= 0.6
Write the equation and find
S_10
of this series:
a_2=8, a_4=20
S_10=10*(2+56)/2=290
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? Use sequences equations! HINT: When he bought the car 0 years have gone by.
$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? HINT:Write out the first few terms and show your equations!
$4774.55
Write the summation notation of the repeating decimal 0.636363...
sum_(1=i)^(oo)0.63(0.01)^(n-1)