IM Alg2.2.26 Lesson: Using the Sum
Recall that for any geometric sequence starting at with a common ratio , the sum of the first terms is given by . Find the approximate sum of the first 50 terms of each sequence:
In 2012, about 71 thousand homes were sold in the United Kingdom. For the next 3 years, the number of homes sold increased by about 18% annually. Assuming the sales trend continues,
How many homes were sold in 2013?
How many homes were sold in 2014?
What information does the value of the expression tell us?
Predict the total number of house sales from 2012 to 2017. Explain your reasoning.
Do these predictions seem reasonable? Explain your reasoning.
Han and Lin each have a method to calculate . Han says this is and concludes that . Lin says that this is a difference of terms in 2 geometric sequences and can be written as . Do you agree with either Han or Lin? Explain your reasoning.
Let’s say you open a savings account with an interest rate of 5% per year compounded annually and that you plan on contributing the same amount to it at the start of every year.
Predict how much you need to put into the account at the start of each year to have over $100,000 in it when you turn 70.
Calculate how much the account would have after the deposit at the start of the 50th year if the amount invested each year were:
$100
$500
$1,000
$2,000
Say you decide to invest $1,000 into the account at the start of each year at the same interest rate. How many years until the account reaches $100,000? How does the amount you invest into the account compare to the amount of interest earned by the account?