Exam 9: Population Growth Models: There Is Strength in Numbers

A population grows in a linear fashion. Suppose that the population begins (i.e. when N=0 ) with 500 individuals and after the tenth generation (i.e. when N=10 ), there are 1800 individuals. What is the value of the common difference d ?

A circular game board is shown below. The board consists of ten different regions. Half of the regions are black and half of the regions are white. Suppose that you start on one of the white regions and you move around the board clockwise. On the first region you place 2 grains of rice, on the 2^nd region you place 4 grains of rice, on the 3^rd regions you place 6 grains of rice, and so on following the pattern. You stop placing grains of rice after you reach the 10^th region. What would be the difference between the total number of grains found on white regions and the total number of grains found on black regions?

Given that represent the term in sequence, then define a recursive rule to be . Find the value of .

Given that A₅=46 and A₇=60 are the 5^th and 7^th terms in an arithmetic sequence, find A₃₀ .

Given that A₁=17 and A₂=22 are the first two terms in an arithmetic sequence, find A₂₅ .

What is the 25^th term in the sequence: 5,7,9,11,13,15, ... .

A geometric sequence has an initial term of 81920 and a common ratio of 0.5 . Based off of this information, what would be the sum of the first twelve terms of this geometric sequence?

On the initial day of class (i.e. N=0 ), a professor counts 480 students as being present in her math class. On the 11^th day of class (i.e. N=10 ) the professor counts 140 students as being present in her math class. If the number of students decreases in a linear fashion, what is the common difference d ?

Jack is fascinated with sea-shells and he collects them every day on the beach. To start off with (i.e. when N=0 ), Jack has 45 sea-shells in his collection. Each day, Jack will add 14 sea-shells to his collection. After 49 days of adding shells, how many shells in total will Jack have?

Given that A₅=7.5 and A₆=3.75 are the fifth and sixth terms in a geometric sequence, find A₁ .

On the initial day of class (i.e. N=0 ), a professor counts 690 students as being present in her math class. On the 6^th day of class (i.e. N=5 ) the professor counts 450 students as being present in her math class. If the number of students decreases in a linear fashion, what is the common difference d ?

Given that A₁₁=35 Find the value of A₁₄ given

Given that A₁=4 and A₂=5 , if A_N represents the N^th term in a sequence, then define a recursive rule to be . Find the value of A₅ .

Given a sequence where find A₃₂ . Give your answer as a fraction in a reduced form.

Given that A₃=18 and A₅=2 are the 3^rd and 5^th terms in a geometric sequence, find A₁ .

A common sheet of copier paper is 0.1 mm in thickness. Each time the paper is folded in half; the total thickness is doubled. Suppose that you were able to fold the sheet of paper in half 25 times. What would be the thickness of this resulting paper mass?

A geometric sequence has an initial term of 8 and a common ratio of 3 . Use this information to find the sum of the first twelve terms of this geometric sequence.

A geometric sequence has an initial term of 4 and a common ratio of 2. Use this information to find the sum of the first ten terms of this geometric sequence.

What is the next term in the sequence, 3,5,9,17,33,65,... .

If A_N represents the N^th term of a sequence, then define a recursive rule as Which of the following equations is a restatement of this rule?