Arithmetic Sequences in Recursive Form

Write a recursive formula for the arithmetic sequence below. What is the value of the sixth term?

15, 11, 7, 3, –1, . . .

• A(1) = 15; A(n) = A(n-1) - 4; A(6) = -9

• A(1) = 15; A(n) = A(n-1) + 4; A(6) = 7

• A(1) = -4; A(n) = A(n-1) + 15; A(6) = -9

• A(1) = -4; A(n) = A(n-1) + 15; A(6) = 29

Tags

CCSS.HSF.BF.A.2

Write a recursive formula for the arithmetic sequence below. What is the value of the sixth term?

–27, –22, –17, –12, . . .

• A(1) = -27; A(n) = A(n - 1) - 5; A(6) = -2

• A(1) = -5; A(n) = A(n - 1) - 27; A(6) = -2

• A(1) = 5; A(n) = A(n - 1) - 27; A(6) = -2

• A(1) = -27; A(n) = A(n - 1) + 5; A(6) = -2

Tags

CCSS.HSF.BF.A.2

Use the recursive definition to find the first four terms of the arithmetic sequence it defines.

A(n) = A(n – 1) + 4; A(1) = –10

• 4, -6, -16, -26, ...

• -10, -14, -18, -22, ...

• -10, -6, -2, 2, ...

• 4, 14, 24, 34, ...

Tags

CCSS.HSF.BF.A.2

Use the recursive definition to find the first four terms of the arithmetic sequence it defines.

A(n) = A(n – 1) – 11; A(1) = 3

• 3, -8, -19, -30, ...

• -11, -8, -5, -2, ...

• 3, 14, 25, 36, ...

• -11, -14, -17, -20, ...

Tags

CCSS.HSF.BF.A.2

Write a recursive definition for the explicit formula.

A(n) = 6 + (n – 1)( –2)

• A(1) = -2, A(n) = A(n - 1) + 6

• A(1) = 6, A(n) = A(n - 1) - 2

• A(1) = -6, A(n) = A(n - 1) + 2

• A(1) = 2, A(n) = A(n - 1) - 6

Tags

CCSS.HSF.IF.A.3

Write a recursive definition for the explicit formula.

A(n) = 5 + (n – 1)(0.5)

• A(1) = 5, A(n) = A(n - 1) + 5

• A(1) = 0.5, A(n) = A(n - 1) + 0.5

• A(1) = 0.5, A(n) = A(n - 1) + 5

• A(1) = 5, A(n) = A(n - 1) + 0.5

Tags

CCSS.HSF.IF.A.3

Write an explicit formula for the recursive formula.

A(n) = A(n – 1) – 6; A(1) = 22

• A(n) = -6 + (n - 1)(22)

• A(n) = 22 + (n - 1)(-6)

• A(n) = 22 + (n - 1) - 6

• A(n) = -6 + (n - 1)22

Tags

CCSS.HSF.BF.A.2

Write an explicit formula for the recursive formula.

A(n) = A(n – 1) + 9; A(1) = –18

• A(n) = -9 + (n - 1)(18)

• A(n) = 9 + (n - 1)(-18)

• A(n) = 18 + (n - 1)(-9)

• A(n) = -18 + (n - 1)9

Tags

CCSS.HSF.BF.A.2

Which is the proper explanation of recursive versus explicit?

• Explicit and Recursive are used to find any term in a sequence.

• Explicit is used to find any term in a sequence and Recursive is used to find the term in a sequence based on the term before it.

• Explicit and Recursive are used to find the term in a sequence based on the term before it.

• Explicit is used to find the term in a sequence based on the term before it and Recursive is used to find any term in a sequence.

Tags

CCSS.HSF.BF.A.2

The first term of an arithmetic sequence is 5. The eleventh term is 125. What is the common difference of the arithmetic sequence?

• 120

• 12

• 10

• 5

Tags

CCSS.HSF.BF.A.2