Consider the two patterns described below.

Question

Pattern Rule Starting
Number
S Add 8 0
T Add 24 0

Which of the following sentences describes the relationship between the corresponding terms in the two patterns?
A.
The terms in pattern S are 3 times smaller than the corresponding terms in pattern T.

B.
The terms in pattern T are 3 times smaller than the corresponding terms in pattern S.

C.
The terms in pattern S are 16 less than the corresponding terms in pattern T.

D.
The terms in pattern T are 16 less than the corresponding terms in pattern S.

Answer 1

To analyze the relationship between the two patterns, we'll first generate the sequences for both patterns S and T based on the given rules.

Pattern S (Add 8, starting at 0):

• First term: 0
• Second term: 0 + 8 = 8
• Third term: 8 + 8 = 16
• Fourth term: 16 + 8 = 24
• Fifth term: 24 + 8 = 32
• The terms are: 0, 8, 16, 24, 32, ...

Pattern T (Add 24, starting at 0):

• First term: 0
• Second term: 0 + 24 = 24
• Third term: 24 + 24 = 48
• Fourth term: 48 + 24 = 72
• Fifth term: 72 + 24 = 96
• The terms are: 0, 24, 48, 72, 96, ...

Now let's compare the corresponding terms in each pattern:

• First term: S(1) = 0, T(1) = 0
• Second term: S(2) = 8, T(2) = 24
• Third term: S(3) = 16, T(3) = 48
• Fourth term: S(4) = 24, T(4) = 72
• Fifth term: S(5) = 32, T(5) = 96

Now, to find the relationship between the two patterns, we can subtract the corresponding terms:

1. For the second term: 8 (S) vs 24 (T):
   • 24 - 8 = 16 (T is 16 more than S)
2. For the third term: 16 (S) vs 48 (T):
   • 48 - 16 = 32 (T is 32 more than S)
3. For the fourth term: 24 (S) vs 72 (T):
   • 72 - 24 = 48 (T is 48 more than S)
4. For the fifth term: 32 (S) vs 96 (T):
   • 96 - 32 = 64 (T is 64 more than S)

From our calculations, we can deduce that the difference between terms in pattern T and pattern S is not constant, but if we focus precisely on the second term, we find:

• For the second term comparison:
  • T(2) - S(2) = 24 - 8 = 16

Thus, the only consistent relationship we can draw from the patterns based on their differences is that the corresponding term T is always greater than S by a multiple of 16 after the first term.

Now, let's evaluate the given answer choices:

• A. The terms in pattern S are 3 times smaller than the corresponding terms in pattern T. (This is not true.)
• B. The terms in pattern T are 3 times smaller than the corresponding terms in pattern S. (This is also not true.)
• C. The terms in pattern S are 16 less than the corresponding terms in pattern T. (This is false; it's the other way around.)
• D. The terms in pattern T are 16 less than the corresponding terms in pattern S. (This is false; it's the opposite.)

The correct answer is:

C. The terms in pattern S are 16 less than the corresponding terms in pattern T.