Understanding Arithmetic Sequences: A Step-by-Step Guide

Find the first four terms of the arithmetic sequence starting at 3 with a common difference of 5.

• A. 3, 7, 12, 17
• B. 3, 8, 13, 18
• C. 3, 5, 8, 13
• D. 3, 9, 15, 21

Answer: (B)

To find the first four terms of an arithmetic sequence, we begin with the first term and continuously add the common difference to generate subsequent terms. In this case, the first term is 3 and the common difference is 5. To find the terms: 1. The first term is given as 3. 2. The second term is calculated by adding the common difference to the first term: \(3 + 5 = 8\). 3. The third term is then calculated by adding the common difference to the second term: \(8 + 5 = 13\). 4. Finally, the fourth term is derived by adding the common difference to the third term: \(13 + 5 = 18\). Thus, the first four terms of the sequence are 3, 8, 13, and 18. This aligns exactly with the selection that includes those values. The option selected shows a clear understanding of how to generate terms in an arithmetic sequence using the specified starting point and common difference, demonstrating the proper method for this kind of problem.

When tackling college math placement tests, one topic that often comes up is the fascinating world of arithmetic sequences. Now, before you roll your eyes and think, “Not another math lesson!”, let’s dive into learning how to find the first four terms of an arithmetic sequence starting at 3 with a common difference of 5. Trust me, by the end, this will feel as easy as pie—well, maybe a little easier than pie!

Let’s Break It Down

So, what exactly is an arithmetic sequence? Simply put, it’s a sequence of numbers where each term is obtained by adding a constant, known as the common difference, to the previous term. Sounds simple, right? You know what? It really is! Now, let’s apply this concept to our problem.

We start with our first term, which is 3. Then, to find the next terms, we continuously add our common difference of 5:

1. First Term: The very first term is given as 3. Easy peasy!

2. Second Term: Here’s where the fun begins! To find the second term, we add our common difference:

[

3 + 5 = 8

]

So, our second term is 8—lucky number, right?

3. Third Term: Let’s keep this going. Now we add 5 to our second term:

[

8 + 5 = 13

]

Voila! The third term is 13. We’re on a roll!

4. Fourth Term: Finally, we add the common difference to our third term:

[

13 + 5 = 18

]

And there we have it—the fourth term is 18.

Wrapping It All Up

So, what are the first four terms of our sequence? They are 3, 8, 13, and 18. If you picked the option that listed these values, congrats! You’ve got a solid understanding of generating terms in an arithmetic sequence using a specified starting point and common difference.

You know, this method isn’t just useful for tests but also comes in handy in real life. Ever noticed how you might save a bit more each month? That’s essentially forming an arithmetic sequence with your savings!

In summary, being familiar with arithmetic sequences not only enhances your math skills but also boosts your confidence when you tackle those placement tests. Don’t fret about the numbers; give them a shot, and before you know it, you’ll have them mastered. Keep practicing, and remember that every term you find brings you one step closer to acing that math placement test!