Question

A number pattern was created by dividing the previous term by 3. If the starting value for the pattern was 135, which of the following shows the resulting pattern?

A.
135, 45, 30, 5...
B.
135, 45, 15, 5...
C.
135, 45, 15, 2...
D.
135, 45, 30, 25...

Answer 1

The number pattern involves dividing each term by 3, starting from 135. The correct sequence is 135, 45, 15, 5, thus Option B is the accurate representation of the pattern.

Step-by-step explanation:

The student is working on a number pattern problem in mathematics, specifically one that involves sequences and series. The question presents a number pattern that was created by dividing the previous term by 3 and starts with the value 135. To continue this pattern, each subsequent term is found by dividing the term before it by 3.

Starting with 135, the first division by 3 gives us 45 (135 ÷ 3 = 45). Continuing this process, the second term (45) is also divided by 3, resulting in 15 (45 ÷ 3 = 15). The third division gives 5 (15 ÷ 3 = 5), and so the pattern will follow as: 135, 45, 15, 5, ...

Therefore, the correct option that shows the resulting pattern is Option B.

Answer 2

B. 135, 45, 15, 5...

Step-by-step explanation:

I'll go in order from 135 using the pattern shown (tᵇ/3)

135 / 3

135 = 120 + 15

135/3 = (120/3) + (15/3)

135/3 = 40 + 5

135/3 = 45

All four answer choices show this, so no elimination yet.

45 / 3

45 = 30 + 15

45/3 = (30/3) + (15/3)

45/3 = 10 + 5

45/3 = 15

A and D show 30 as term 3, so they are out.

15 / 3

15/3 = 5

C shows 2 as term 4, so that is also out.

This leaves B as the correct answer.