Mastering Sequences: Unraveling the Highest Number in a Series

Have you ever wondered what makes sequences of numbers tick? Well, you're in for a treat! Let’s dive into the world of consecutive numbers starting from 5, and discover how to find the highest number in that sequence. Whether you’re prepping for the GMAT or just love math, understanding these sequences is a fantastic skill to have in your toolkit.

So, here’s the setup: we have a sequence of numbers that starts at 5, and we want to find out what the highest number is in the first 125 terms of that sequence. Easy enough, right?

Let me explain how this works. The first few numbers in our sequence look like this:

• n1 = 5
• n2 = 6
• n3 = 7
• And so on.

Notice what's happening here? Each number increases by 1 from the previous number, forming a neat little chain. If we keep going, we can say that the nth term (or in this case, the 125th term) can be calculated by taking our starting number and adding the index minus one.

So, what's that look like mathematically? Grab a pen because here comes the magic:

n125 = 5 + (125 - 1)

This gives us:

n125 = 5 + 124 = 129.

Voila! The highest number in this sequence is 129. Pretty straightforward, right? Each step just adds to our starting point — it’s like a friendly game of hopscotch where each square represents a number, and you're simply counting your jumps.

Isn’t it fascinating how patterns work in math? It's kind of like when you're trying to predict the weather based on past conditions – if you recognize the trends, you can make educated guesses for the future!

Now, imagine you're on the GMAT, and a question like this pops up. You don't have to panic. Just remember this little formula, and you'll nail it! Each term corresponds directly to its position in the sequence, giving you a clear path to the answer. So whether it's this problem or a variation of it, knowing how to navigate sequences will boost your confidence.

To wrap things up, when you're faced with problems involving sequences, take a moment. Break it down, look for the pattern, and you'll discover that the math is often simpler than it seems at first glance. Just like that, you’re one step closer to mastering the GMAT! Keep practicing, stay curious, and don't shy away from number games — they might just surprise you!