https://file.aiquickdraw.com/mathbot/file/17243352330525b7jyd1g.jpg

Find the missing term in each every sequence term

Let's analyze the sequences provided in the image:

### Sequence 40: `-1, ____, ____, ____, 31, 39` (second space)
To find the missing terms in this sequence, we need to identify a pattern.

#### Step 1: Calculate the differences between the known terms:
- \(31 - 39 = -8\)
  
Given the pattern in typical sequences, it's likely the sequence is arithmetic or geometric, but since the difference is not constant, this might involve a different logic. However, without more information, let's assume it's an arithmetic sequence for simplicity.

#### Step 2: Work backward:
If the sequence has a constant difference:
- Next difference (let's assume) is also \(-8\), so \(39 - 8 = 31\).
- If we go further back, the difference should remain \(-8\), \(31 - 8 = 23\).

The pattern might be:
\[ \ldots, 23, 31, 39 \]

However, since the earlier numbers could differ, more logic might be involved. For simplicity, without additional terms, the most common solution is an arithmetic sequence.

### Sequence 41: `-1, ____, ____, ____, 31, 39` (third space)
This appears to be identical to Sequence 40 but asks for the third missing space. Following the same pattern:
- The term just before 31 (in Sequence 40) is 23.
- If we assume the pattern applies to the term before that, it might be \(15\), resulting in:
\[ -1, \ldots, 15, 23, 31, 39 \]

### Sequence 42: `13, ____, ____, ____, -11, -17` (first space)
Similarly, let's identify the pattern:
- The difference between \(-11\) and \(-17\) is \(-6\).
- The difference before this could be a constant value:
\[ 13, \ldots, \ldots, \ldots, -11, -17 \]

Given these, the third difference should likely be \(-6\) or another consistent value. Suppose we try \(-6\):
\[ -11 + 6 = -5\), hence:
\[ -5 + 6 = 1 \), thus:
\[ 1 + 6 = 7 \), finally:
\[ 13 - 6 = 7 \]

This leads us to suspect that the first term is either \(7\).

### Sequence 43: `13, ____, ____, ____, -11, -17` (second space)
This might follow similar logic as above:
\[ 13, 7, 1, -5, -11, -17 \).

So, the second term should be `7`.

### Sequence 44: `13, ____, ____, ____, -11, -17` (third space)
Following the same logic, the third term should be `1`.

### Final Answers:
1. **Sequence 40 (second space)**: Likely `23` or based on more complex logic (requires assumption about the pattern).
2. **Sequence 41 (third space)**: Likely `15`.
3. **Sequence 42 (first space)**: Likely `7`.
4. **Sequence 43 (second space)**: Likely `7`.
5. **Sequence 44 (third space)**: Likely `1`.

Would you like further details on how to confirm these sequences or have any questions? Here are some additional related problems:

1. How can you identify the type of sequence (arithmetic, geometric, etc.)?
2. What is the general formula for the \(n\)th term in an arithmetic sequence?
3. How do you calculate missing terms in a geometric sequence?
4. What are other common types of sequences and their properties?
5. How do you approach solving sequences with mixed or non-linear patterns?

**Tip**: Always consider different possible patterns (arithmetic, geometric, quadratic) when dealing with sequences.

Explore how to find the missing term in arithmetic sequences. This problem-solving guide provides step-by-step solutions for identifying the missing terms in given sequences, covering arithmetic sequence patterns and formulas. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation