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MATH 108 Fall 2016 Quiz 7

Problem 1. 3 pts. Evaluate the sum

∑ 2𝑛2 5

𝑛=1

− 2𝑛 − 5

Problem 2. 5 pts.

2A. Find the explicit formula for the general term an of the sequence given below. That is, find

the rule that will allow you to calculate each term directly, without a recursive formula.

2B. Use your general rule to find the 800th term of the sequence.

$15.24, $14.82, $14.40, $13.98,…

Problem 3. 4 pts. Write the sum using sigma notation:

−2

9 +

4

8 −

6

7 +

8

6 −

10

5 +

12

4

Problem 4. 6 pts. On Jan 1, 2015, there were 1000 deer living in a national park. On Jan 1, 2016

there were 10% more deer than the year before. On Jan 1 of each year, it is estimated that the

deer population will be another 10% above the previous year’s count.

A.Write the first 4 terms of the sequence of annual deer population counts.

B. Find the general rule for the sequence of annual deer population counts.

C. What is the deer population expected to be on Jan 1, 2030?

Problem 5. 6 pts. Consider the sequence 144, 108, 81, 60.75, ….

5A. Find the formula for the general term an of the sequence. That is, find the rule that will allow

you to calculate each term directly, without a recursive formula.

5B. Find the 14th term of the sequence.

5C. Find S∞, which is the sum of an infinite number of terms of the sequence.

Problem 6. 6 pts.

A book on each year’s Breakthroughs in Mathematics is published annually. The 2016 edition

costs $22.00. Each year, the price will increase by $2.50 over the previous year’s price.

A. Find the general rule for the sequence of the book prices.

B. Determine what the price will be in 2040.

C. If you buy a book each year from 2016 to 2040, how much will have you spent in total?