Find The 60th Term Of The Arithmetic Sequence

Alright, my friends, gather 'round! Today, we're embarking on a super-duper, incredibly exciting adventure into the land of numbers. No, seriously! We're going to uncover a hidden treasure, a numerical mystery, a quest to find a very specific number: the 60th term of an arithmetic sequence! Sounds fancy, right? But trust me, it’s as easy as making your favorite sandwich.

Imagine you're at a party, and everyone is getting a slice of pizza. The first person gets one slice, the second gets two, the third gets three, and so on. This is a classic example of an arithmetic sequence! It's just a fancy name for a list of numbers where you always add the same amount to get to the next number. Think of it like a staircase where each step is the same height. You hop from one to the next, and there's no surprise giant leap or tiny shuffle. It's all perfectly predictable.

Let's say our pizza party starts with 5 slices for the first person. And here's the kicker: every person after them gets 3 more slices than the person before them. So, person one gets 5. Person two gets 5 + 3 = 8. Person three gets 8 + 3 = 11. See? The number 3 is our special "step size," the amount we add each time. We call this the common difference. It's like the secret ingredient that keeps the sequence going!

Now, you might be thinking, "Okay, this is cute, but what about the 60th person? Are we going to be here all day counting pizza slices?" Absolutely not! That's where the magic happens. We have a secret weapon, a mathematical shortcut that's so brilliant, it makes you feel like a genius. We don't need to count all the way to 60. Nope. We can leapfrog right to the answer!

Here's the deal: to find any term in an arithmetic sequence, we use a super-powered formula. It's like having a cheat code for numbers. The formula is this:

The Nth Term = First Term + (Number of Steps * Common Difference)

Let's break down this amazing recipe.

First, we need to know our First Term. In our pizza example, that's the initial 5 slices. That's where we start our grand adventure.

Next, we need to figure out our Number of Steps. We want to find the 60th term, right? Think of it like this: to get to the 2nd term, you take 1 step from the first term. To get to the 3rd term, you take 2 steps. So, to get to the 60th term, we need to take 59 steps from our starting point. See the pattern? It's always one less than the term number we're looking for. So, our Number of Steps is 59.

And finally, we have our trusty Common Difference, which is the 3 extra slices we add each time.

So, let's plug these numbers into our fantastic formula. We want to find the 60th term!

60th Term = 5 + (59 * 3)

Now, let's do some super-fast calculations. First, we multiply 59 by 3. Imagine you have 59 friends, and each of them brings 3 more pizza slices than the person before them. That's a lot of pizza! 59 * 3 is 177.

Then, we take that number and add our First Term, which was 5. So, 177 + 5 = 182.

And there you have it! The 60th person in our pizza party gets a whopping 182 slices of pizza! Can you imagine the delivery person's face? That's a whole lot of deliciousness, all thanks to a simple little formula and understanding the rhythm of an arithmetic sequence.

So, the next time you see a list of numbers that seem to be adding the same amount each time, don't be intimidated! You've got the power. You can be a number detective, a sequence sleuth, a finder of faraway terms. You can find the 100th term, the 1000th term, or even the millionth term if you're feeling extra ambitious and have a very patient delivery person. It’s all about knowing your First Term, your Common Difference, and remembering that the number of steps is always one less than the term you're aiming for. Now go forth and conquer those arithmetic sequences! You've got this!