Find a formula for the th term of the
arithmetic sequence.
First term 11
Common difference 5

Hint: The coefficient of n is the common difference.

The formula for the th term of an arithmetic sequence is given by , where is the first term and is the common difference. For your sequence, we have and . Substituting these values in gives us:

Now simplifying that, we get:

And there you have it! The th term formula is

!

This shows the beauty of arithmetic sequences where each term builds upon the last with a consistent increment. You can practically see how this formula allows you to calculate any term in the sequence effortlessly! Whether you’re counting reaching your goals or counting objects, having a reliable formula helps keep you organized and focused!

When applying the formula in real life, think of it as a way to plan your savings. If you save a fixed amount of money every month, you can calculate how much money you’ll have saved after months using the same formula structure. If you start with $11 and add $5 each month, you can easily keep track of your growing savings balance! It’s a simple yet effective way of managing personal finance over time.