Question

The first term of an arithmetic sequence is -5, and the tenth term is 13. Find the common difference.

1. 8/9
2. 1.8
3. 2

Answer 1

`\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=-5\\ n=10\\ a_(10)=13 \end{cases} \\\\\\ a_(10)=a_1+(10-1)d\implies 13=-5+(10-1)d \\\\\\ 13=-5+9d\implies 18=9d\implies \cfrac{18}{9}=d\implies \boxed{2=d}`