Question

Rule 1: Add 3 starting from 0. Rule 2: Add 9 starting from 0. Complete the first 5 terms using the rules. How are the corresponding terms related? (4 points)

Each term in the second sequence is one-third the corresponding term in the first sequence.
Each term in the first sequence is three times the corresponding term in the second sequence.
Each term in the first sequence is one-sixth the corresponding term in the second sequence.
Each term in the second sequence is three times the corresponding term in the first sequence.

Answer 1

Using Rule 1, we can generate the first 5 terms as:

0, 3, 6, 9, 12

Using Rule 2, we can generate the first 5 terms as:

0, 9, 18, 27, 36

We can observe that each term in the second sequence is three times the corresponding term in the first sequence. Therefore, the correct answer is:

Each term in the second sequence is three times the corresponding term in the first sequence.

Answer 2

d) Each term in the second sequence is three times the corresponding term in the first sequence.

Explanation:

Given rules for two arithmetic sequences:

• Rule 1: Add 3 starting from 0.
• Rule 2: Add 9 starting from 0.

The first 5 terms of the first sequence (rule 1) can be found by adding 3 to the previous term, where the initial term is zero:

`a_1=0`

`a_2=a_1+3=0+3=3`

`a_3=a_2+3=3+3=6`

`a_4=a_3+3=6+3=9`

`a_5=a_4+3=9+3=12`

Therefore, the first 5 terms of the first sequence are: 0, 3, 6, 9, 12.

The first 5 terms of the second sequence (rule 2) can be found by adding 9 to the previous term, where the initial term is zero:

`a_1=0`

`a_2=a_1+9=0+9=9`

`a_3=a_2+9=9+9=18`

`a_4=a_3+9=18+9=27`

`a_5=a_4+9=27+9=36`

Therefore, the first 5 terms of the second sequence are: 0, 9, 18, 27, 36.

Comparing each term of the second sequence with the corresponding term of the first sequence, we can see that each term of the second sequence is 3 times the corresponding term of the first sequence:

`0 * 3 = 0`

`3 * 3 = 9`

`6 * 3 = 18`

`9 * 3 = 27`

`12 * 3 = 36`

Therefore, the correct answer option is:

• d) Each term in the second sequence is three times the corresponding term in the first sequence.