Question

Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.

A(n) = 12 + (n – 1)(3)

A.12, 21, 39

B. 0, 9, 27

C. 12, 24, 42

D. 3, 24, 27

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} \end{cases}\\\\ -------------------------------\\\\`


`\bf A(n)=12+(n-1)(3)\qquad \begin{cases} n=n^(th)\ term\\ 12=\textit{first term's value}\\ 3=\textit{common difference} \end{cases} \\\\\\ n=1,4\ and\ 10\implies \begin{cases} A(\underline{1})=12+(\underline{1}-1)(3)\\ A(\underline{4})=12+(\underline{4}-1)(3)\\ A(\underline{10})=12+(\underline{10}-1)(3) \end{cases}`