\[ \begin{aligned} a_{n} & =a_{1}+(n-1) d & & \text { General Formula for Arithmetics } \\ & =13+(n-1)(-5) & & a_{1}=13 \text { and } d=-5 \\ & =13+(-5) n+50 & & \text { Distributive Property } \\ & =-5 n+180 & & \text { Simplify. } \end{aligned} \] Reset Part B Find the 20th term In the sequence. \( \square \)

To find the 20th term in the arithmetic sequence defined by the formula \( a_n = -5n + 180 \), we can simply substitute \( n = 20 \): \[ a_{20} = -5(20) + 180 = -100 + 180 = 80 \] So, the 20th term in the sequence is \( 80 \). --- Let’s get nostalgic! This formula for finding the nth term of an arithmetic sequence has roots that go back to ancient mathematics, where mathematicians used simple patterns to solve problems related to trade and land measuring. The beauty of arithmetic sequences is that they offer predictable outcomes - a true gem in mathematical history! Now, speaking of real-world applications, mastering arithmetic sequences can come in handy when calculating finances, like savings over time. Imagine you save a fixed amount each month; using this formula, you can easily predict how much you'll have after a certain number of months. It's all about planning for the future with confidence!