Consider the sequence - 8, - 4, 0, 4, 8, 12, ellipsis. Select True or False for each statement. A recursive rule for the sequence is f (1) = - 8; f (n) = - 4 (n - 1) for all n ≥ 2. A True B False An explicit rule for the sequence is f (n) = - 8 + 4 (n - 1). A True B False The tenth term is 28.

A recursive rule for the sequence is f (1) = - 8; f (n) = - 4 (n - 1) for all n ≥ 2 is "FALSE"

An explicit rule for the sequence is f (n) = - 8 + 4 (n - 1) is "TRUE"

The tenth term is 28 is "TRUE"

Step-by-step explanation:

Statement (1)

While the first part [f (1) = - 8] is TRUE, the second part [f (n) = - 4 (n - 1) for all n ≥ 2] would only be true if the sequence ends at the second term.

Check: Since the fifth term of the sequence is 8, then f (5) = 8

From the statement,

f (5) = - 4 (5 - 1)

f (5) = - 4 * 4 = - 16

:. f (5) ≠ 8

Statement (2)

f (n) = - 8 + 4 (n - 1) is TRUE

Check: The fifth term of the sequence is 8 [f (5) = 8]

From the statement,

f (5) = - 8 + 4 (5 - 1)

f (5) = - 8 + 4 (4)

f (5) = - 8 + 16 = 8

:. f (5) = 8

Statement (3)

f (10) = 28 is TRUE

Since the explicit rule is TRUE, use to confirm if f (10) = 28:

f (10) = - 8 + 4 (10 - 1)

f (10) = - 8 + 4 (9)

f (10) = - 8 + 36

f (10) = 28

:. f (10) = 28