Arithmetic Sequences

Which of the following is the correct formula in finding the nth term of an arithmetic sequence?

• a_n = a₁ + (n - 1)d

• a_n = a₁ + (n + 1)d

• a_n = a₁ - (n - 1)d

• a_n = a₁ +- (n + 1)d

Which of the following sequence is an arithmetic sequence?

• 5, 12, 21, 32, 45, . . .

• 3, 6, 12, 24, 48, . . .

• –8, –5, –2, 1, 4, . . .

• 12, 7, 11, 6, 10, 5, . . .

Which of the following sequence is NOT an arithmetic?

• 25, 13, 1, –11, –23, . . .

• 9, 15, 21, 27, 33, . . .

• –12, –4, 4, 12, 20, 28, . . .  

• –4, 5, 18, 35, 56, 81, . . .

Select the explicit rule that represents the sequence.

• a_n = 6 + 5(n - 1)

• a_n = 4 + 6(n - 1)

• a_n = 6 - 4(n - 1)

Given the sequence:

25, 21, 17, 13,...

Write the explicit equation that models the sequence.

• a_n = 25 + (n-1)4

• a_n = 29 + (n-1)(-4)

• a_n = 25 +(n-1)(-4)

• a_n = 29 +(n-1)(4)

What is a₁ in the following sequence?

-6, -14, -22, -30, ...

• -6

• -14

• -22

• -30

What is the common difference of the following sequence?

7, 27, 47, 67,...

• 10

• 20

• 3

• -20

Write the explicit formula for the sequence.

9, 5, 1, -3, ...

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

• -1, 7, 15
• -5, 2, 9
• 3, 12, 21
• -65, -73, -81

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

• -16, -21, -26, -31
• 5, -11, -27, -43
• -16, -80, -500, -200
• -16, -11, -6, -1