The first term of the arithmetic sequence is $\frac {2 } { 3 }$ and the common difference is $\left( - \frac { 2 } { 3 } \right\}$Which term of this sequence is $- \frac { 20 } { 3 }$?
A) $10 ^ { \mathrm { th} } \text { term }$
B) $12 ^ { \text {th } } \text { term }$
C) $13 ^ { \text {th } } \text { term }$
D) $16 ^ { \mathrm { th } } \text { term }$
E) $6 ^ { \mathrm { th } } \text { term }$

Question

Quizplus · Accepted Answer

The nth term of an arithmetic sequence is given by $a_n = a_1 + (n-1)d$, where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number. Substituting $a_1 = \frac{2}{3}$, $d = -\frac{2}{3}$, and $a_n = -\frac{20}{3}$, we get $-\frac{20}{3} = \frac{2}{3} + (n-1)(-\frac{2}{3})$. Solving for $n$, we find $n = 12$.

The First Term of the Arithmetic Sequence Is 23\frac {2 } { 3 }32​

The First Term of the Arithmetic Sequence Is $\frac {2 } { 3 }$