Mastering Sequences: Unraveling the Highest Number in a Series

In a sequence of consecutive numbers starting from 5, what is the highest number in the sequence n1, n2, n3, ..., n125?

• A. 124
• B. 125
• C. 129
• D. 130

Answer: (C)

In this sequence, the numbers are consecutive and start from 5. To find the highest number in the sequence of the first 125 terms (n1, n2, n3, ..., n125), we need to realize that n1 corresponds to the first term, which is 5, and each subsequent term increases by 1. Therefore, the first few numbers in the sequence would be: - n1 = 5 - n2 = 6 - n3 = 7 - ... - n125 = 5 + (125 - 1) Here, we see that to get to the 125th number, we add 124 to the starting point of 5: n125 = 5 + 124 = 129. This calculation shows that the highest number in this sequence of 125 consecutive numbers starting from 5 is indeed 129. Each number is simply the starting point plus the index minus one, which confirms that the answer of 129 is accurate and reflects the pattern of consecutive integers starting from 5.

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!