M1T2: Lesson 2 Skills Practice- Arithmetic and Geometric Sequences

Determine the common difference and the next 3 terms in each arithmetic sequence.

Enter values separated by commas, no spaces.

8, 14, 20, 26,

common difference:

-24, -14, -4, 6,

common difference:

$\frac{3}{5}, \frac{4}{5}, 1, \frac{6}{5},$

common difference:

12, 16.5, 21, 25.5,

common difference:

-101, -112, -123, -134,

common difference:

3.8, 5.1, 6.4, 7.7,

common difference:

Determine the common ratio and the next 3 terms in each geometric sequence.

Enter values separated by commas, no spaces.

3, 9, 27, 81,

common ratio:

512, 256, 128, 64,

common ratio:

5, -10, 20, -40,

common ratio:

3000, 300, 30, 3,

common ratio:

2, -2, 2, -2,

common ratio:

0.2, 1.2, 7.2, 43.2,

common ratio:

Determine whether each given sequence is arithmetic or geometric. Write the next 3 terms of each sequence. (no spaces, separated by commas)

$a_{n}=a_{n-1}+4$ where $a_{1}=4$ and n is a whole number greater than 1.

Enter A for arithmetic or G for geometric:

Next 3 terms:

$m_{n}=-0.8+m_{n-1}$, where $m_{1}=-7.2$and n is a whole number greater than 1.

Enter A for arithmetic or G for geometric.

Next 3 terms:

$p_{n}=4 \cdot p_{n-1}$, where$p_{1}=3$and n is a whole number greater than 1.

Enter A for arithmetic or G for geometric.

Next 3 terms:

$k_{n}=-2 \cdot k_{n-1}$, where $k_{1}=9$and n is a whole number greater than 1.

Enter A for arithmetic or G for geometric.

Next 3 terms:

$f(n)=\frac{1}{2}f(n-1)$, where $f(1)=1.5$ and n is a whole number greater than 1.

Enter A for arithmetic or G for geometric.

Next 3 terms.

$h(n)=3+h(n-1)$, where $h(1)=15$ and n is a whole number greater than 1.

Enter A for arithmetic or G for geometric.

Next 3 terms.

Consider the first 2 terms of the sequence -6, 18, ...

Determine the next 5 terms in the sequence if the sequence is arithmetic. Then, write the function to represent the arithmetic sequence.

next 5 terms:

$A_{n}=$

Determine the next 5 terms in the sequence if the sequence is geometric. Then, write a function to represent the geometric sequence.

next 5 terms:

$A_{n}=$

Josh updates his blog regularly with trivia questions for readers to answer. The month he started this, there were 8 trivia questions on his blog. The next month, there were 19 trivia questions on his blog. The month after that, there were 30 trivia questions on his blog.

Think about the number of trivia questions on Josh's blog each month. Describe the pattern.

Determine how many trivia questions will be on Josh's blog during months 4, 5, and 6.

Contestants on a popular game show have an opportunity to randomly select a cash prize in 6 hidden containers. The highest possible cash prize is $25,000. The next highest prize is $5000, and the one after that is $1000.

Think about how the value of the prize changes from one container to the next. Describe the pattern.

Determine the prize values in the remaining containers.

Enter each function into your graphing calculator to determine the shape of its graph. Then, complete the table based on the characteristics of the function family.

Function:$5x^{2}-2.8x+40$

Function family:

Increasing, decreasing, or both:

Absolute max or min:

Curve or line:

Function: $f(x)=30x+550$

Function family:

Increasing, decreasing, or both:

Absolute max or min:

curve or line: