A sequence of numbers starts at 5 and increases by 3 each time. What is the 50th term of this sequence?
["Understanding an Arithmetic Sequence: Finding the 50th Term Starting from 5 with a Common Difference of 3", "Have you ever wondered how sequences of numbers follow a clear mathematical pattern? One simple yet powerful example is an arithmetic sequence — a series where each term increases by a fixed value. In this article, we’ll explore an arithmetic sequence that starts at 5 and increases by 3 each time. We’ll also discover how to calculate the 50th term effortlessly using a straightforward formula.", "### What is an Arithmetic Sequence?", "An arithmetic sequence is defined by a starting number, called the first term, and a constant difference between consecutive terms. For example, if the first term is a₁ = 5 and the common difference is d = 3, the sequence progresses as:", "5, 8, 11, 14, 17, …", "Every term increases consistently by 3. This predictable pattern makes arithmetic sequences useful in math, finance, computer science, and daily problem-solving.", "### The General Formula for the nth Term", "The position of any term in an arithmetic sequence can be found using the formula:", "[\na_n = a_1 + (n - 1) \ imes d\n]", "Where:\n- ( a_n ) = the nth term\n- ( a_1 ) = first term (in this case, 5)\n- ( d ) = common difference (here, 3)\n- ( n ) = term number (we want the 50th term, so ( n = 50 ))", "### Calculating the 50th Term", "Plug the known values into the formula:", "[\na_{50} = 5 + (50 - 1) \ imes 3\n]", "First, calculate the exponent:", "[\n50 - 1 = 49\n]", "Then multiply by the common difference:", "[\n49 \ imes 3 = 147\n]", "Finally, add the first term:", "[\na_{50} = 5 + 147 = 152\n]", "### Conclusion", "The 50th term of the sequence that starts at 5 and increases by 3 each time is 152. Recognizing arithmetic sequences and using their formula helps solve a variety of real-world problems quickly and accurately. Whether you're working on math homework, coding, or budgeting, mastering this concept empowers your analytical skills.", "If you enjoy pattern recognition and mathematical sequences, exploring more formulas like this opens doors to deeper understanding and practical applications in everyday life."]
