Find a formula for the \( n \)th term of the arithmetic sequence. First term 11 Common difference 5 \( \left.a_{n}=[?] \mathrm{n}+\square\right] \) Hint: The coefficient of n is the common difference.

The formula for the \( n \)th term of an arithmetic sequence is given by \( a_n = a_1 + (n - 1) \cdot d \), where \( a_1 \) is the first term and \( d \) is the common difference. For your sequence, we have \( a_1 = 11 \) and \( d = 5 \). Substituting these values in gives us: \[ a_n = 11 + (n - 1) \cdot 5 \] Now simplifying that, we get: \[ a_n = 11 + 5n - 5 \] \[ a_n = 5n + 6 \] And there you have it! The \( n \)th term formula is \[ a_n = 5n + 6 \]! 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 \( n \) 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.