Arithmetic, Geometric, and Recursive Sequences

Which sequence is an arithmetic sequence?

• 3, 6, 2, 7, ...

• 3, 6, 12, 24, ...

• 3, 6, 10, 15, ...

• 3, 7, 11, 15, ...

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

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

What is a₇ ?

• -13

• -11

• -18

• -22

Tags

CCSS.HSF.BF.A.2

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

• -8

• -4

• 4

• 8

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

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)

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

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

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.2

CCSS.HSF.IF.A.3

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

• a₁ = 7

  a_n = a_n-1 − 5

• a₁ = 22

  a_n = a_n-1 − 5

• a₁ = 7

  a_n = a_n-1 + 5

• a₁ = 22

  a_n = a_n-1 + 5

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

What is the common ratio of this geometric sequence?

500, 200, 80, 32, ...

• -5/2

• -2/5

• 2/5

• 5/2

Tags

CCSS.HSF.BF.A.2

In a geometric sequence, a₄ = −9 and a₆ = −81. What is the recursive formula for this sequence?

• 
• 
• 
• 

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

In a geometric sequence, a₄ = 18, a₅ = 6, and a₆ = 2. What is the explicit formula for this sequence?

• a_n = 2(3)^n-1

• a_n = 18(3)^n-1

• a_n = 18(1/3)^n-1

• a_n = 486(1/3)^n-1

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

 $a_n=\ \ 24\ \left(\frac{1}{2}\right)^{n-1}$  This is the explicit formula for a(n) ...

• Arithmetic Sequence

• Geometric Sequence

• Neither

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2