Learning Check 6- Seq/Series

What type of formula/rule is the following?

a₁ = 4, a_n = a_n-1(1/2)

• Recursive, Geometric

• Explicit, Geometric

• Recursive, Arithmetic

• Explicit, Arithmetic

What type of formula/rule is the following?

a₁ = -18, a_n = a_n-1+(1/2)

• Recursive, Geometric

• Explicit, Geometric

• Recursive, Arithmetic

• Explicit, Arithmetic

What type of formula/rule is the following?

a_n = 12(1/2)^n-1

• Recursive, Geometric

• Explicit, Geometric

• Recursive, Arithmetic

• Explicit, Arithmetic

Does the following sequence converge?

a_n = 12(1/2)^n-1

• yes, because you're repeatedly multiplying by a fraction so it approaches 0

• no, because you're repeatedly multiplying by a fraction it doesn't approach a single value

• cannot tell from the info given

How do you identify a geometric sequence? (Assuming you aren't told in the directions that it's geometric.)

• You add a common value, d.

• You multiply by a common value, r

• Your numbers get smaller

What is r for the following geometric sequence definition?

a_n = 12(1/2)^n-1

• 1

• 12

• 1/2

• n-1

What is r for the following sequence?

6, -12, 24, -48,...

• 2

• -2

• 1/2

• -1/2

Use the definition of a partial sum to determine what is the S₃ for the sequence

a_n = 2(3)^n-1

• 26

• 18

• 2

How would you solve the following without the sum function on your calculator?

• a₁₃ + ... + a₁₉

• a₁₂ + a₁₃ + ... + a₁₈

• a₁₂ + a₁₃ + ... + a₁₉

How would you solve the following using partial sums?

• S₁₈ - S₁₁

• S₁₉ - S₁₁

• S₁₉ - S₁₂