Let’s solve the problem step by step:

Problem Breakdown:

1. Height of the mountain above sea level:
   $784 + \frac{1}{5} \, \text{m}$
   Convert the mixed fraction into a decimal:
   $784 + \frac{1}{5} = 784.2 \, \text{m}$.

2. Height of the tower:
   $38 + \frac{1}{25} \, \text{m}$
   Convert the mixed fraction into a decimal:
   $38 + \frac{1}{25} = 38.04 \, \text{m}$.

3. Height of the lightning rod:
   $3 + \frac{4}{5} \, \text{m}$
   Convert the mixed fraction into a decimal:
   $3 + \frac{4}{5} = 3.8 \, \text{m}$.

4. Total height above sea level:
   Add all the heights together:
   $784.2 + 38.04 + 3.8 = 826.04 \, \text{m}$.

Final Answer:

The very top of the lightning rod is 826.04 meters above sea level.

Let me know if you want more detailed steps or have any further questions. Here are related questions to explore:

1. How do you convert mixed fractions into decimals?
2. What is the general formula for combining heights in a similar scenario?
3. Can you explain how to round off results if required for precision?
4. How is the sea level used as a reference in elevation problems?
5. How do you add fractions with different denominators?

Tip: Always double-check calculations involving fractions and decimals to avoid small mistakes.