Solution: The sequence starts at 0 and increases by 5 each time. The nth term is $ a_n = 5(n-1) $. Setting $ 5(n-1) = 100 $, solve for $ n $:

["Understanding Linear Sequences: How to Solve for n Using the Formula", "When studying sequences in mathematics, one key concept is linear sequences — sets of numbers where each term increases by a constant difference. In this article, we’ll explore a simple yet illustrative linear sequence and demonstrate how to find the position of a specific term using a straightforward algebraic equation.", "---", "### What Is the Sequence?", "The sequence starts at 0 and increases by 5 each time. This means the terms proceed as:", "0, 5, 10, 15, 20, …", "This is a linear sequence where each term follows the pattern defined by the formula:", "[\na_n = 5(n - 1)\n]", "Here:\n- ( a_n ) represents the nth term,\n- ( n ) is the term number (starting at 1),\n- The sequence begins at ( a_1 = 0 ), since ( a_1 = 5(1 - 1) = 5 \ imes 0 = 0 ).", "---", "### Why This Formula Works", "Since the sequence increases by 5 each time and starts at 0, the first term corresponds to ( n = 1 ), the second to ( n = 2 ), and so on. Because the value grows from 0 by adding 5 per term, the nth term can be expressed as:", "[\na_n = 5 \ imes (n - 1)\n]", "This formula captures both the starting point of 0 and the step size of 5.", "---", "### Solving a Common Problem", "Suppose we want to find which term in this sequence equals 100. We set up the equation:", "[\n5(n - 1) = 100\n]", "Now solve for ( n ):", "1. Divide both sides by 5:", "[\nn - 1 = \frac{100}{5} = 20\n]", "2. Add 1 to both sides:", "[\nn = 20 + 1 = 21\n]", "---", "### Conclusion: The 21st Term Is 100", "The sequence increases by 5 starting from 0, so the 21st term is:", "[\na_{21} = 5(21 - 1) = 5 \ imes 20 = 100\n]", "This logical approach — modeling real-world patterns with algebraic equations — helps students and learners grasp the power of sequences and linear relationships.", "---", "Key Takeaway:\nLinear sequences like this one follow a clear pattern governed by a formula. By setting up a simple equation, such as ( 5(n - 1) = 100 ), you can solve for the position of any term efficiently — a foundational skill in algebra and beyond.", "---", "Keywords: linear sequence, arithmetic sequence, nth term formula, solve for n, 5(n−1) = 100, step-by-step solution, repetitive increase, mathematical pattern"]