I see the image you uploaded is a math activity where you are asked to find the missing terms in arithmetic sequences. Let me help solve the problems one by one:

1. 29, ___, ___, 15, ...

   • To find the missing terms, let's first determine the common difference. The difference between 29 and 15 is $29 - 15 = 14$. Since there are two missing terms, we divide this difference by 3: $\frac{14}{3} \approx 4.67$ So, the common difference is about $-4.67$.

   Now, subtract this difference from 29: $29 - 4.67 = 24.33$ Subtract again from 24.33: $24.33 - 4.67 = 19.67$ So the missing terms are approximately 24.33 and 19.67.

2. 2, ___, 4, ___, 8, ...

   • Here, the terms increase by a common difference. The difference between 2 and 4 is $4 - 2 = 2$, and the difference between 4 and 8 is $8 - 4 = 4$. This suggests the sequence alternates between increasing by 2, then 4. The second term would be: $2 + 2 = 4$ And the next term after 4 would be: $4 + 4 = 8$ So, the missing terms are 3 and 6.

3. 19, ___, ___, -31, ...

   • The difference between 19 and -31 is: $19 - (-31) = 19 + 31 = 50$ Divide the difference by 3 to find the common difference: $\frac{50}{3} \approx 16.67$ Subtract this from 19 to get the second term: $19 - 16.67 = 2.33$ Subtract again: $2.33 - 16.67 = -14.34$ So the missing terms are approximately 2.33 and -14.34.

4. ___, -4, ___, -68, ...

   • The difference between -4 and -68 is: $-4 - (-68) = -4 + 68 = 64$ Divide by 2 to find the common difference: $\frac{64}{2} = 32$ Adding this to -4 gives us: $-4 + 32 = 28$ Subtracting 32 from -68 gives: $-68 - 32 = -100$ So the missing terms are 28 and -100.

5. 32, ___, ___, 71, ...

   • The difference between 32 and 71 is: $71 - 32 = 39$ Divide this by 3 to find the common difference: $\frac{39}{3} = 13$ Add 13 to 32: $32 + 13 = 45$ Add 13 again: $45 + 13 = 58$ So the missing terms are 45 and 58.

Would you like further details on any of the sequences? Here are 5 related questions:

1. How do you recognize an arithmetic sequence?
2. What is the formula for finding the common difference in an arithmetic sequence?
3. Can you find the sum of terms in an arithmetic sequence?
4. How do you determine the $n$-th term of an arithmetic sequence?
5. How does the process differ for geometric sequences?

Tip: Always verify your common difference by applying it to all terms to ensure consistency!