Write an expression for the apparent $n$th term of the sequence. (Assume that $n$ begins with 1.)
$$- 5 , - 2,1,4,7$$
A) $a _ { n } = - 8 n + 3$
B) $a _ { n } = ( - 1 ) ^ { n } ( 3 n - 8 )$
C) $a _ { n } = 3 n$
D) $a _ { n } = 3 ^ { n } - 8$
E) $\quad a _ { n } = 3 n - 8$

Question

Quizplus · Accepted Answer

We can observe that each term in the sequence is 3 more than 3 times the previous term. That is, if we let the first term be denoted by $a_1$, then $a_2 = 3a_1 + 3$, $a_3=3a_2+3$, and so on. Hence, we can obtain $a_n$ by the formula $a_n=3(n-1)+a_1$, where $a_1$ is the first term. Solving for $a_1$ using the first term given (which is $a_1=-5$), we get $a_n=3n-8$ as our final answer, which is option $\boxed{	ext{(E)}}$.

Write an Expression for the Apparent nnn Th Term of the Sequence

Write an Expression for the Apparent $n$ Th Term of the Sequence