Question

Which of the following choices is the simple formula for the nth term of the following arithmetic sequence?

7,3,-1,-5,-9,...

A. 4n+1
B. -4n+11
C. 5n+4
D. -4n+1
E.4n+11

Answer 1

`\bf 7~~,~~\stackrel{7-4}{3}~~,~~\stackrel{3-4}{-1}~~,~~\stackrel{-1-4}{-5}~~,~~\stackrel{-5-4}{-9}~~,~~...`

so namely, the "common difference" d = -4, and the first term a₁ = 7.


`\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}\\ ----------\\ d=-4\\ a_1=7 \end{cases} \\\\\\ a_n=7+(n-1)(-4)\implies a_n=7+(4-4n) \\\\\\ a_n=11-4n\implies a_n=-4n+11`