Write a formula for the general term (the nth term)of the arithmetic sequence. Then use the formula for $r a _ { n }$ to find $a _ { 20 }$ , the 20th term of the sequence.
-$$\mathrm { a } _ { 1 } = - \frac { 1 } { 5 } , \mathrm {~d} = \frac { 3 } { 5 }$$
A) $a _ { n } = \frac { 3 } { 5 } n - \frac { 4 } { 5 } ; a _ { 20 } = \frac { 56 } { 5 }$
B) $a _ { n } = \frac { 3 } { 5 } n - \frac { 1 } { 5 } ; a _ { 20 } = \frac { 59 } { 5 }$
C) $a _ { n } = - \frac { 1 } { 5 } n + \frac { 4 } { 5 } ; a _ { 20 } = - \frac { 16 } { 5 }$
D) $a _ { n } = - \frac { 1 } { 5 } n + \frac { 3 } { 5 } ; a _ { 20 } = - \frac { 17 } { 5 }$

Question

Quizplus · Accepted Answer

The formula for the nth term of an arithmetic sequence is $a_n = a_1 + (n - 1)d$. Substituting $a_1 = -\frac{1}{5}$ and $d = \frac{3}{5}$, we get $a_n = -\frac{1}{5} + (n - 1)\frac{3}{5} = \frac{3}{5}n - \frac{4}{5}$. For $a_{20}$, substituting $n = 20$ into the formula gives $a_{20} = \frac{3}{5} \times 20 - \frac{4}{5} = \frac{56}{5}$.

Write a Formula for the General Term (The Nth Term)of ranr a _ { n }ran​

Write a Formula for the General Term (The Nth Term)of $r a _ { n }$