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155 Sequences

Last updated over 4 years ago
17 questions

An introduction to Sequences

1

What is a sequence?

Common type of sequence #1:
1

Find the next term: 8, 14, 20, ...

1

How did you find the next term? (What did you notice about the numbers?)

1

Graph the points: \{(1,8), (2,14), (3,20)...\}
1. Hit the +
2. choose the table

1

What do you notice about the graph?

1

Use what you noticed to write an equation that represents the numbers in the list.

1

Use your equation to find the 52nd term in the list.

1

This type of sequeence was linear - and is called "arithmetic"
Create your own arithmetic sequence.

1

The number you add each time is called the "common difference".
What number did you add in your sequence?
Graph your sequence (in a table, use the "+").
How does the common difference relate to the line that is graphed?

1

Write the equation for your sequence.

Common type of sequence #2:
1

Find the next term: 256, 64, 16, 4, ...

1

How did you find the next term? (What did you notice about the numbers?)

1

Graph the points \{(1,256), (2,64), (3,16), ...)\}

1

On the table you made for [7], hold down the button next to y_1.
Toggle over the slide next to "line" to turn it on.
What do you notice about the graph?

1

Use what you noticed to write an equation that represents the numbers in the list.

1

Use your equation to find the 15th term in the list.
Write your answer as a fraction.

This type of sequence was exponential - and is called "geometric".
When we last did exponential we used y=a(b)^x.

Now the base is called the "common ratio".

Instead of using a (the inital value or y-intercept), we will use the first value = a_1.
1

The geometric sequence equation is thus
y=

Between today and tomorrow, you can do the first five sections of DeltaMath.