Question

-37,-35, -33, -31 find the 40 term

Answer 1

if you notice, it goes form -37, to -35, to -33 and so on.

so is really adding 2 to get the next term,

`\bf -37~~,~~\stackrel{-37+2}{-35}~~,~~\stackrel{-35+2}{-33}~~,~~\stackrel{-33+2}{-31}........`

so, the common difference is 2, and the first term is of course -37.

`\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=-37\\ d=2\\ n=40 \end{cases} \\\\\\ a_(40)=-37+(40-1)2\implies a_(40)=-37+78\implies a_(40)=41`