The problem involves a sequence with a two-step term-to-term rule:

1. Start at 6.
2. Multiply by 2, then add 3 each time.

Step-by-Step Solution:

• First term (T₁): $6$ (given).
• Second term (T₂): $6 \times 2 + 3 = 15$ (also given).
• Third term (T₃): $T₂ \times 2 + 3 = 15 \times 2 + 3 = 30 + 3 = 33$

Thus, the next term in the sequence is 33.

Do you want further details on sequences or additional practice problems? Here are some questions for exploration:

1. What would the fifth term in this sequence be?
2. How does the two-step rule change if the "add 3" step is replaced with "subtract 3"?
3. Can you write a general formula for the nth term in this sequence?
4. How would the sequence look if the starting value were 10 instead of 6?
5. Can you create a sequence with a similar rule but using division instead of multiplication?

Tip: When solving term-to-term sequences, carefully follow each step in the rule for accuracy!