Warmup- Recursive and Explicit Functions

Write the recursive rule for the arithmetic sequence
82, 76, 70, 64, ...

• a₁=82; a_n = a_n-1-6
• a₁=64; a_n = a_n-1-6
• a₁=82; a_n = a_n-1+6
• a₁=64; a_n = a_n-1+6

An arithmetic sequence is given below.

2, 9, 16, 23, ...

Which is the explicit formula for the n^th term a_n?

(Look at the choices carefully! You may have to simplify your equation to get the correct choice!)

• a_n = -7n+9

• a_n = 7n-5

• a_n = 7n-9

• a_n = -7n+5

Select the explicit rule that represents the sequence.

• a(n) = 14(-3)(n - 1)

• a(n) = 3 + (n - 1)(14)

• a(n) = 14 + (n - 1)(-3)

• a(n) = -3 + (n - 1)(14)

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1 - 1

• 14

• 13

• 17

• 16

Write a Next/Now rule for the table

• Next=Now - 16 Starting at 32
• Next=Now - 16 Starting at 0
• Next=Now ÷ 4 Starting at 0
• Next=Now × ½ Starting at 32

What is the common ratio or difference of the sequence: 5, 20, 80, 320, ...

• r = 4

• d = 15

• r = 5

• d = 60

Identify this type of sequence: 5, 20, 80, 320, ...

• Arithmetic

• Geometric

• Neither

A geometric sequence has a₁ = 3 and r = 2. What is the Explicit Rule for a_n and use it to find the 10th term.

• a_n = 3 + 2(n-1)

  a₁₀ = 21

• a_n = 2(3)^n-1

  a₁₀ = 39366

• a_n = 3(2)^n-1

  a₁₀ = 1536

• a_n = 2 + 3(n-1)

  a₁₀ = 29