Simple Arithmetic and Geometric Sequences

a₄ = 3 and a₁₀ = -39. Find the common difference of the arithmetic sequence.

• -6

• -7

• -8

• -9

a₃ = 225 and a₅ = 5625

Find the common ratio of the geometric sequence.

• 3

• 4

• 5

• 25

Which sequence is an arithmetic sequence?

• 3, 6, 2, 7, ...

• 3, 6, 12, 24, ...

• 3, 6, 10, 15, ...

• 3, 7, 11, 15, ...

This is an arithmetic sequence. 5, 2, –1, –4, . . .

What is a₇ ?

• -13

• -11

• -18

• -22

Given the arithmetic sequence: 22, 17, 12, 7, . . . . What is the recursive formula that models the sequence?

• f (1) = 7

  f (n) = f (n − 1) − 5

• f (1) = 22

  f (n) = f (n − 1) − 5

• f (1) = 7

  f (n) = f (n − 1) + 5

• f (1) = 22

  f (n) = f (n − 1) + 5

Which sequence is a geometric sequence with a common ratio of 2?

• 5, 3, 1, -1, ...

• 5, 7, 9, 11, ...

• 5, 10, 20, 40, ...

• 5, 15, 45, 135, ...

In a certain arithmetic sequence, a₅ = 12 and a₆ = 16. What is a₁ ?

• -8

• -4

• 4

• 8

The first term of an arithmetic sequence is b and the second term is c. What is the explicit formula to find the n^th term of the sequence?

• a_n = b + (n − 1) c

• a_n = c + (n − 1) b

• a_n = b + (n − 1) (b − c)

• a_n = b + (n − 1) (c − b)

The explicit formula for a sequence is a_n = 5 − 3n. What is the value of a₂₂ ?

• a₂₂ = -61

• a₂₂ = 61

• a₂₂ = -1

• a₂₂ = -51

In an arithmetic sequence, the third term is 1 and the ninth is 49. What is the explicit formula for the sequence?

• a_n = 8n − 15

• a_n = −8n − 15

• a_n = 8n − 23

• a_n = −8n − 23