The exercise in the image asks the following:

1. Write the next two terms of the sequences from the given number sequences.
   • Sequence a: $8.5, 2, -1$
   • Sequence c: $-15, -11, -7$

It then includes some guiding questions:

• Is the given sequence an arithmetic sequence?
• If yes, what is the common difference, and what are the next two terms of the sequence?
• If not, what pattern can be observed in the sequence?

Let's analyze both sequences:

1. Sequence a: $8.5, 2, -1$

   • To check if it is arithmetic, we find the differences between consecutive terms:
     • $2 - 8.5 = -6.5$
     • $-1 - 2 = -3$
   • The differences are not equal, so this is not an arithmetic sequence. We would need further pattern analysis to predict the next terms, potentially by checking other mathematical rules or sequences.

2. Sequence c: $-15, -11, -7$

   • Find the differences:
     • $-11 - (-15) = 4$
     • $-7 - (-11) = 4$
   • The differences are equal, so this is an arithmetic sequence with a common difference of 4.
   • To find the next two terms, add 4 to the last term:
     • Next term: $-7 + 4 = -3$
     • Term after: $-3 + 4 = 1$
   • The next two terms are $-3$ and $1$.

Would you like further details or have any questions?

Related questions:

1. How do we determine if a sequence is arithmetic?
2. What are the other types of sequences besides arithmetic?
3. How can we determine the general formula for an arithmetic sequence?
4. What could be the possible pattern for Sequence a if it's not arithmetic?
5. What is the significance of identifying the type of sequence?

Tip:

When dealing with sequences, always check for a consistent difference or ratio between terms to identify the pattern or rule.