To extrapolate the given sequence, we first analyze the pattern between the terms:

Differences between consecutive terms:

1. $4000 - 0 = 4000$
2. $9000 - 4000 = 5000$
3. $14980 - 9000 = 5980$
4. $21920 - 14980 = 6940$
5. $29800 - 21920 = 7880$
6. $38600 - 29800 = 8800$
7. $48310 - 38600 = 9710$
8. $58900 - 48310 = 10590$
9. $70360 - 58900 = 11460$
10. $82680 - 70360 = 12320$
11. $95820 - 82680 = 13140$
12. $109790 - 95820 = 13970$
13. $124550 - 109790 = 14760$
14. $140100 - 124550 = 15550$
15. $156420 - 140100 = 16320$

Observations:

The differences themselves form an increasing arithmetic sequence, with a common difference of $980$ (e.g., $5000 - 4000 = 1000, 5980 - 5000 = 980,$ etc.).

Formula for the differences:

Let the difference at the $n$-th position be $d_n$. The formula for $d_n$ is: $d_n = 4000 + (n - 1) \cdot 980$

Generating the next 10 terms:

Using the last term in the sequence ($156420$) as the starting point, we calculate the next differences and add them cumulatively.

1. $d_{16} = 4000 + 15 \cdot 980 = 16480$
2. $d_{17} = 4000 + 16 \cdot 980 = 17460$
3. $d_{18} = 4000 + 17 \cdot 980 = 18440$
4. $d_{19} = 4000 + 18 \cdot 980 = 19420$
5. $d_{20} = 4000 + 19 \cdot 980 = 20400$
6. $d_{21} = 4000 + 20 \cdot 980 = 21380$
7. $d_{22} = 4000 + 21 \cdot 980 = 22360$
8. $d_{23} = 4000 + 22 \cdot 980 = 23340$
9. $d_{24} = 4000 + 23 \cdot 980 = 24320$
10. $d_{25} = 4000 + 24 \cdot 980 = 25300$

Adding these to the previous term:

1. $156420 + 16480 = 172900$
2. $172900 + 17460 = 190360$
3. $190360 + 18440 = 208800$
4. $208800 + 19420 = 228220$
5. $228220 + 20400 = 248620$
6. $248620 + 21380 = 270000$
7. $270000 + 22360 = 292360$
8. $292360 + 23340 = 315700$
9. $315700 + 24320 = 340020$
10. $340020 + 25300 = 365320$

Final Sequence:

$0, 4000, 9000, 14980, 21920, 29800, 38600, 48310, 58900, 70360, 82680, 95820, 109790, 124550, 140100, 156420, 172900, 190360, 208800, 228220, 248620, 270000, 292360, 315700, 340020, 365320$

Would you like a detailed explanation of the process or a graph of this sequence?

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5 Follow-Up Questions:

1. Would you like to derive a formula for the $n$-th term of the sequence?
2. Can we analyze how quickly the sequence grows as $n$ increases?
3. Do you want to calculate specific properties like the sum of these terms?
4. Should we graph the sequence to visualize its growth?
5. Can this pattern be applied to a real-world problem you're solving?

Tip:

When working with sequences, always check for patterns in differences or ratios to identify arithmetic or geometric progressions.