calculate the 50th structure is the general rule is n^2+1

To calculate the 50th term of the sequence given by the formula \( n^2 + 1 \), simply substitute \( n = 50 \) into the formula:

\[
n^2 + 1 = 50^2 + 1
\]

Calculate the square of 50:

\[
50^2 = 2500
\]

Then, add 1:

\[
2500 + 1 = 2501
\]

So, the 50th term of the sequence is **2501**.

Would you like any more details or have any questions? Here are some related questions:

1. What would be the 100th term in the sequence \( n^2 + 1 \)?
2. How does the sequence behave as \( n \) increases?
3. Can you derive the sum of the first 50 terms of this sequence?
4. What is the difference between the 50th and 49th terms?
5. How would the sequence change if the formula was \( n^2 - 1 \) instead?

**Tip:** Sequences defined by quadratic functions, like \( n^2 + 1 \), grow rapidly as \( n \) increases due to the square term.

Learn how to calculate the 50th term of the sequence defined by the formula n^2 + 1. Follow a step-by-step solution to find the specific term and understand the growth pattern of the sequence. Suitable for high school students studying sequences and quadratic functions.

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