Sequences and Series

Term

In a sequence each number is called a term.

The dots at the end mean the sequence continues forever.

a₁ is the first term

a₂ is the second term

a₃ is the third term and so on...

a_n is the nth term (we will find the equation for the nth term in the next lesson)

Multiple Choice

What does a₁ represent?

• Any term

• First term

• Last term

Multiple Choice

What kind of sequence is the pattern 15, 17, 20, 24, 29, ...?

• Arithmetic
• Geometric
• Neither

Multiple Choice

For each sequence, state if it is arithmetic, geometric, or neither.
−34, −26, −18, −10, −2, ... 

• Arithmetic
• Geometric
• Neither

Multiple Choice

What kind of sequence is the pattern 400, 200, 100, 50, 25, ...?

• Arithmetic
• Geometric
• Neither

Multiple Choice

What is the Rule for this sequence?
97, 86, 75, 64, ...

• +8
• +11
• -11
• -8

Multiple Choice

Is the sequence geometric? If so, identify the common ratio.

6, 12, 24, 48

• yes, 2

• yes, -2

• yes, 4

• no

Multiple Choice

Given the sequence 2, 8, 14, 20, 26, ... What is the common difference?

• 2

• 4

• 6

• 8

Multiple Choice

Write the recursive formula for 6, 17, 28, 39, 50....

• a_n=a_n-1+11

  a₁=6

• a_n=a_n-1-4

  a₁=6

• a_n=a_n-1+9

  a₁=6

• a_n=a_n-1+6

  a₁=6

Multiple Choice

Find the explicit formula:

-3, -33, -63, -93, ...

• a_n = -3 - 30(n -1)

• a_n = -3 + 30(n -1)

• a_n = -30 - 3(n -1)

• a_n = -30 + 3(n -1)

Multiple Choice

What is the common ratio for the sequence:

28, 14, 7, 3.5...

• 2

• 1/2

• -14

• -7

Multiple Choice

• A

• B

• C

• D

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Sometimes sequences are described in subscript notation.

Given $$a_1=-5$$  and $$a_n=a_{n-1}+3$$  , what are the first 4 terms in the sequence?

• -5, -2, 1, 4

• -5, -8, -11, -14

• 3, -2, -7, -12

• 3, -15, 75, -375