Arithmetic Sequence Rule

Which sequence(s) represent an arithmetic sequence?

• a and e

• a, b, and e

• b, c, and d

• b

The explicit rule for arithmetic sequence is a_n = a₁ + d(n − 1), what does the d represent.

• common denominator

• common difference

• common divider

• uncommon difference

In the recursive rule for the arithmetic sequence a_n =  a_{(n − 1)} + d, the (n − 1) represent the ________________.

• next term

• current term

• previous term

• first term

Complete the Table.

• 25, 32, 39, 46

• 7, 32, 57, 82

• 32, 39, 46, 53

• 7, 14, 21, 28

An arithmetic sequence has a₁=2 and d=4. What is the Explicit Rule for a_n and use it to find the 20^th term.

• a_n = 2 - 4(n-1)

  a₂₀ = 82

• a_n = 2 + 4(n-1)

  a₂₀ = 78

• a_n = 2(4)^n-1

  a₂₀ = 2199023255552

• a_n = 4 + 2(n-1)

  a₂₀ = 42

• 315

• 330

• 345

• 360

Is this an arithmetic sequence?

• yes

• maybe

• sometimes

• no

Write the explicit rule for this situation.

• f(n) = 35 + 3(n − 1)

• f(n) = 35 −3(n − 1)

• f(n) = 3 + 35(n − 1)

• f(n) = −3 + 35(n − 1)

Write the recursive rule for this situation.

• f(n) = f(n − 1) + 58, n ≥ 2

• f(n) = 58 + 7(n − 1)

• f(n) = 58 − 7(n − 1)

• f(n) = f(n − 1) + 7, n ≥ 2

What is the common difference?

• −16

• 84

• 16

• 0