Question

What’s the nth term for 25,20,15,10,5

Answer 1

so it goes from 25 to 20 to 15 and so on, clearly we get the next term by simply subtracting 5 from the current one, meaning, the common difference is -5, and of course, the first term is 25.

`\bf n^(th)\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^(th)\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ a_1=25\\ d=-5 \end{cases} \\\\\\ a_n=25+(n-1)(-5)\implies a_n=25+5-5n\implies \boxed{a_n=30-5n}`