https://file.aiquickdraw.com/mathbot/file/17274805928899wo2ccjz.jpg

Let's analyze the sequence from the image: 15, 16, 20, 29, ..., ...

We will try to find a pattern and predict the next two terms of the sequence.

- From 15 to 16, there is an increase of **+1**.
- From 16 to 20, there is an increase of **+4**.
- From 20 to 29, there is an increase of **+9**.

These increments correspond to the sequence of perfect squares (1², 2², 3²). So, it seems like the next increment could be **+16** (which is 4²) and then **+25** (which is 5²) for the following term.

- The next term after 29 should be \( 29 + 16 = 45 \).
- The term after 45 should be \( 45 + 25 = 70 \).

So, the next two terms are **45 and 70**. Let's now match this with the options provided:

- a. 20, 30
- b. 30, 40
- c. 40, 50
- d. 50, 60
- e. 60, 70

The correct answer is **e. 60, 70**.

Would you like more details or have any other questions?

### 5 Related Questions:
1. How do you identify different patterns in sequences?
2. What is the role of perfect squares in number sequences?
3. Could there be another possible interpretation for this sequence?
4. How can we generalize this sequence to find the nth term?
5. Can arithmetic and geometric progressions apply here?

### Tip: 
When analyzing sequences, always check if the differences between terms follow a recognizable pattern like arithmetic, geometric, or involving perfect squares.

15, 16, 20, 29, ..., ...
Options:
 a. 20, 30
 b. 30, 40
 c. 40, 50
 d. 50, 60
 e. 60, 70

Learn how to recognize and solve a number sequence involving perfect squares. The sequence starts with 15, 16, 20, and 29. By identifying the pattern of increasing differences (perfect squares), we predict the next two terms as 45 and 70. This problem is suitable for students in Grades 6-8.

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