In the following exercises and problems you will be able to:

model investment and annuity problems;

explain the difference between sequences and series;

solve exercises applying concepts of the sum of sets of terms of a sequence, and

solve problems related to annuities using probate or series.

Note: In the event that the result is decimal, you will round it to two decimal places.

1.Explain the difference between a sequence and a series (5 marks). Provide clear and complete explanations and interpretations. You should base yourself on the properties of sequences and series and use formal mathematical language and notation to present your explanation. Mention at least two applications of business administration where it is important to take into account the difference between sequences and series

2.Let the arithmetic sequence be defined by the formula

un = 11 + (n-1) 6

Apply the concepts of the sum of terms of a sequence to determine the sum of the 6th to the 20th term (inclusive).

3.A $ 100 deposit is made into a college fund at the beginning of each month for 10 years. The fund earns 9% annual interest, compounded monthly and paid at the end of the month. How much is in the account right after the last deposit?

4.At the beginning of each month, $ 200 is deposited into a retirement fund. The fund earns 6% annual interest, compounded monthly and paid into the account at the end of the month. How much is in the account if deposits are made over 10 years?

5.An annuity pays $ 15,000 per year. Due to inflation, each year a dollar is worth what $ 0.970 was worth the previous year. Payment is made at the beginning of each year. What is the present value of the annuity if it is paid over three years (starting immediately)?