Sequences

1) Match each term with its definition. To match, just click on a box from the left column and then click it's match from the box on the right column. Sequence A set of numbers that follows a pattern. Term Each number in a sequence. Arithmetic Sequence A sequence followed by adding a fixed number to the previous term. Geometric Sequence A sequence found by multiplying the previous term by a fixed number. Common Difference The fixed number added to the previous term in an arithmetic sequence. Common Ratio The fixed number multiplied to the previous term in a geometric sequence. 2) Sorting Sequences Sort the following into Arithmetic Sequences, Geometric Sequences, or Neither by clicking each box and choosing where it belongs. Arithmetic 2, 8, 14, 20,... 90, 80, 70, 60,... -1, -5, -9, -13,... 24, 19, 14, 9, ... -18, -15, -12, -9, -6, ... Geometric 1, 5, 25, 125, ... 1000, 500, 250,... 1, -3, 9, -27,... 1.5, 3.0, 6.0, 12.0, ... 2, -4, 8, -16 Neither 1, 2, 4, 7, 11, ... 1, 4, 9, 16, 25, ... -2, -1, 2, 7, 14,... -13, -6, -1, 2, 3,... 3) Sorting Linear vs Exponential Tables If the y - values in a table have a common difference and form an arithmetic sequence, then the table represents a linear relationship.If the y - values in a table have a common ratio and form a geometric sequence, then the table represents an exponential relationship.Sort the following tables into linear functions and exponential functions. Linear Function Exponential Function 4) Sorting Linear Situations If a situation shows an increase or decrease by a common difference (arithmetic sequence), then it is best modeled by a linear function.If a situation shows an increase or decrease by arate (geometric sequence), then it is best modeled by an exponential function.Which situations are best modeled by a linear function? Which situations are best modeled by an exponential function? Linear A salesperson initially earns $50,434 dollars per year and receives a yearly raise of $675. A wildlife park has 35 zebras and sends 1 zebra to another wildlife park each year. The population of a town is 66,666 people and decreases by 160 people each year. Exponential Enrollment at a school is initially 454 students and grows by 3% per year. A customer borrows $450 at 5% interest compounded annually. The value of a house is $546,768 and decreases by 3% each year. 5) Matching Arithmetic Sequences with it's common Difference The sequences below are arithmetic. Match each sequence with its common difference. 5, 8, 11, 14, ... d = 3 -17, -12, -7, -2, ... d = 5 -8, -11, -14, -17, ... d = -3 6) Matching Geometric Sequences with it's common ratio The sequences below are geometric. Match each sequence with its common ratio. 2, 6, 18, 54, ... r = 3 1, -5, 25, -125, ... r = -5 -3, -12, -48, -192, ... r = 4