Question

Consider the two patterns described below.


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.