Question

Write an equation for the nth term of the arithmetic sequence 12,14,16,18

Answer 1

The nth term of an arithmetic sequence can be represented by the formula: a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference between the terms. In this case, the equation for the nth term is: a_n = 12 + (n-1)2

Step-by-step explanation:

The nth term of an arithmetic sequence can be represented by the formula: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference between the terms.

In this case, the first term (a1) is 12 and the common difference (d) is 2. Therefore, the equation for the nth term is: an = 12 + (n-1)2

Answer 2

`\bf 12~~,~~\stackrel{12+2}{14}~~,~~\stackrel{14+2}{16}~~,~~\stackrel{16+2}{18}\qquad \qquad \stackrel{\textit{common difference}}{d = 2} \\\\[-0.35em] ~\dotfill\\\\ n^(th)\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^(th)\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\ \cline{1-1} a_1=12\\ d = 2 \end{cases} \\\\\\ a_n=12+(n-1)2\implies a_n=12+2n-2\implies a_n=2n+10`