Find the 100th terms of the arthmetic sequence whose first 5 terms are given. 76,80,84,88,92

To find the 100th term of an arithmetic sequence, we need two key pieces of information:

1. The first term of the sequence (\(a_1\)).
2. The common difference (\(d\)) between the terms.

### Step 1: Identify the first term and the common difference

From the given sequence: \(76, 80, 84, 88, 92\),

- The first term \(a_1 = 76\).
- The common difference \(d\) can be found by subtracting the first term from the second term:

\[
d = 80 - 76 = 4
\]

### Step 2: Use the formula for the nth term of an arithmetic sequence

The formula to find the \(n\)-th term (\(a_n\)) of an arithmetic sequence is:

\[
a_n = a_1 + (n - 1) \times d
\]

### Step 3: Find the 100th term

Substitute \(a_1 = 76\), \(d = 4\), and \(n = 100\) into the formula:

\[
a_{100} = 76 + (100 - 1) \times 4
\]

Simplify the expression:

\[
a_{100} = 76 + 99 \times 4
\]

\[
a_{100} = 76 + 396
\]

\[
a_{100} = 472
\]

### Conclusion

The 100th term of the arithmetic sequence is **472**.

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

1. What is the sum of the first 100 terms of this arithmetic sequence?
2. How can we derive the formula for the \(n\)-th term of an arithmetic sequence?
3. What would the 50th term be in this sequence?
4. If the common difference were negative, how would the sequence change?
5. Can you find the arithmetic mean of the first 5 terms of the sequence?

**Tip:** When working with arithmetic sequences, always check the common difference to ensure it's constant throughout the sequence.

Find the 100th term of the arithmetic sequence whose first 5 terms are given: 76, 80, 84, 88, 92.

Discover how to find the 100th term of the arithmetic sequence with first 5 terms 76, 80, 84, 88, 92. This detailed solution covers the key algebraic concepts and the arithmetic sequence formula, making it perfect for students in Grades 7-9.

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