Let's solve for the next three terms of each sequence, along with the process:

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(i) Sequence: 3, 7, 11, 15, ...

This is an arithmetic sequence, where the difference between consecutive terms is constant. To find the common difference:

• $7 - 3 = 4$
• $11 - 7 = 4$
• $15 - 11 = 4$

The common difference, $d$, is 4.

To find the next three terms:

• Next term = $15 + 4 = 19$
• Next term = $19 + 4 = 23$
• Next term = $23 + 4 = 27$

The next three terms are: 19, 23, 27.

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(ii) Sequence: 50, 45, 40, 35, ...

This is also an arithmetic sequence, where the difference between consecutive terms is constant. To find the common difference:

• $45 - 50 = -5$
• $40 - 45 = -5$
• $35 - 40 = -5$

The common difference, $d$, is -5.

To find the next three terms:

• Next term = $35 - 5 = 30$
• Next term = $30 - 5 = 25$
• Next term = $25 - 5 = 20$

The next three terms are: 30, 25, 20.

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(iii) Sequence: -2, 1, 4, 7, ...

This is another arithmetic sequence, with the common difference calculated as:

• $1 - (-2) = 3$
• $4 - 1 = 3$
• $7 - 4 = 3$

The common difference, $d$, is 3.

To find the next three terms:

• Next term = $7 + 3 = 10$
• Next term = $10 + 3 = 13$
• Next term = $13 + 3 = 16$

The next three terms are: 10, 13, 16.

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Summary of Results:

1. Sequence (i): 19, 23, 27
2. Sequence (ii): 30, 25, 20
3. Sequence (iii): 10, 13, 16

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Would you like further clarification on any of the steps? Here are some related questions:

1. How can you verify the common difference in an arithmetic sequence?
2. What are the general formulas to find the nth term of an arithmetic sequence?
3. Can these sequences be extended indefinitely, and how would you express that mathematically?
4. How can you calculate the sum of the first n terms of an arithmetic sequence?
5. How do geometric sequences differ from arithmetic sequences?

Tip: When solving for the next terms of an arithmetic sequence, it's always helpful to first find the common difference (or ratio for geometric sequences), and then simply add (or multiply) by that value to extend the sequence.