Arithmetic Sequences
What is the formula for an Arithmetic Sequence?
an = a1 + (n - 1)d
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=57(0.66)x
Decay, 34%
What are the first four terms of the following sequence?
an=3*(-1/3)n-1
3, -1, (1/3), (-1/9)
What is the formula for the sum of a geometric series.
Sn=(a1-a1rn))/(1-r)
Ian invested $13,000 in an account paying an interest rate of 5.7% compounded annually. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 12 years?
$25280
Write an explicit formula for the following sequence:
-24, -20, -16, ...
an=-24+4(n-1)
A person invested $310 in an account growing at a rate allowing the money to double every 9 years. How much money would be in the account after 14 years, to the nearest dollar?
$911
Write a recursive formula for the following sequence: 8, -4, 2, -1, ...
a1=8
an=an-1(-1/2)
Find the sum of the first 10 terms of this sequence: 3, 12, 48, ...
1048575
Allison invested $87,000 in an account paying an interest rate of 1.5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 9 years?
$99574.70
How many terms are in the following sequence? 1,3,5,7...43
21 terms
Given the following growth where x represents years, what is the monthly growth rate? Round to the nearest tenth.
y=810(1.23)xx
1.7% monthly growth rate
What is the 17th term of the following sequence? 65, 45.5, 31.85, 22.295, ...
0.22
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 :-)
Adrian invested $68,000 in an account paying an interest rate of 6.2% compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 18 years?
$207560
What are the first four terms of the following sequence?
T1=12
Tn=Tn-1 + (-23)
12, -11, -34, -57
Given the following function, where x is in years, write the function with a weekly rate.
y=6000(1.74)x
y=6000(1.0107)52x
What is the equation to find the 89th term of this sequence?
3, 15, 75, 375
an=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
Lily is going to invest $670 and leave it in an account for 17 years. Assuming the interest is compounded continuously, what interest rate, to the nearest hundredth of a percent, would be required in order for Lily to end up with $920?
1.87%
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
In a lab experiment, 8700 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 21 hours. How long would it be, to the nearest tenth of an hour, until there are 20200 bacteria present?
t≈25.5
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
Caleb invested $2,600 in an account paying an interest rate of 5.7% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $6,880?
17.1 years