If a sequence starts at 5 and increases by 4 each time, what is the 12th term?
["Understanding an Arithmetic Sequence: Finding the 12th Term Starting at 5 with a Common Difference of 4", "If you’ve ever worked with sequences in mathematics, you’ve likely encountered arithmetic sequences — patterns where each number increases by a constant amount, known as the common difference. One common example starts at a given initial value and adds the same number repeatedly. In this article, we’ll explore a specific arithmetic sequence that begins at 5 and increases by 4 each step to find the 12th term.", "### What Is an Arithmetic Sequence?", "An arithmetic sequence follows a simple rule: each term is obtained by adding a fixed difference to the previous term. The general formula for the (n)th term of an arithmetic sequence is:", "[\na_n = a_1 + (n - 1) \ imes d\n]", "Where:\n- (a_n) is the (n)th term\n- (a_1) is the first term\n- (d) is the common difference\n- (n) is the term number", "### Applying the Formula to the Given Sequence", "In our example:\n- The first term (a_1 = 5)\n- The common difference (d = 4)\n- We want to find the 12th term, so (n = 12)", "Plugging these values into the formula:", "[\na_{12} = 5 + (12 - 1) \ imes 4\n]", "[\na_{12} = 5 + 11 \ imes 4\n]", "[\na_{12} = 5 + 44\n]", "[\na_{12} = 49\n]", "### Conclusion", "The 12th term in the sequence that starts at 5 and increases by 4 each time is 49. Understanding this straightforward formula helps quickly determine any term in an arithmetic sequence without listing all prior values. Whether you're solving math problems, coding algorithms, or analyzing patterns, recognizing arithmetic sequences and applying this formula efficiently makes computations faster and clearer.", "---", "Keywords for SEO: arithmetic sequence, geometric progression, sequence formula, 12th term calculation, common difference, find nth term, mathematical patterns, linear growth sequence.\nMeta Description: Learn how to find the 12th term of an arithmetic sequence that starts at 5 and increases by 4 each time using the formula (a_n = a_1 + (n-1) \ imes d). Get step-by-step calculation and explanation."]
