The sequence you're describing appears to follow a pattern of the form:

$a_n = 193 + (n+6) \times 2^{30}$

Let's break this down:

• The first term corresponds to $n = 1$, which is $193 + 7 \times 2^{30}$.
• The second term corresponds to $n = 2$, which is $193 + 8 \times 2^{30}$.
• The third term corresponds to $n = 3$, which is $193 + 9 \times 2^{30}$.

So, the $n$-th term of the sequence is:

$a_n = 193 + (n+6) \times 2^{30}$

Want to go further? Here are some related questions:

1. How would you calculate the 5th term of this sequence?
2. How can we generalize sequences with exponential growth like this one?
3. What happens if you replace the 2^30 term with a different base, say 3?
4. How does the sequence change if we subtract instead of adding the exponential term?
5. How do we find the sum of the first $n$ terms of such a sequence?

Tip: When dealing with exponential sequences like this, recognizing the pattern in the multiplier (in this case, $2^{30}$) is key to finding the general term efficiently.