Find the general term of the arithmetic sequence.
-$$\frac { 1 } { 6 } , \frac { 2 } { 3 } , \frac { 7 } { 6 } , \frac { 5 } { 3 } , \frac { 13 } { 6 } , \ldots$$
A) $a _ { n } = \frac { n - 2 } { 6 }$
B) $a _ { n } = \frac { n + 1 } { 6 }$
C) $a _ { n } = \frac { 3 n + 1 } { 6 }$
D) $a _ { n } = \frac { 3 n - 2 } { 6 }$

Question

Quizplus · Accepted Answer

The common difference of the sequence is $\frac{2}{3}$. The first term $a_1 = \frac{1}{6}$. The general term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$, where $d$ is the common difference. Substituting $a_1 = \frac{1}{6}$ and $d = \frac{2}{3}$, we get $a_n = \frac{1}{6} + (n - 1)\frac{2}{3} = \frac{1}{6} + \frac{2n - 2}{3} = \frac{1 + 4n - 4}{6} = \frac{3n - 2}{6}$.

Find the General Term of the Arithmetic Sequence 16,23,76,53,136,…\frac { 1 } { 6 } , \frac { 2 } { 3 } , \frac { 7 } { 6 } , \frac { 5 } { 3 } , \frac { 13 } { 6 } , \ldots61​,32​,67​,35​,613​,…

Find the General Term of the Arithmetic Sequence $\frac { 1 } { 6 } , \frac { 2 } { 3 } , \frac { 7 } { 6 } , \frac { 5 } { 3 } , \frac { 13 } { 6 } , \ldots$