Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a20,
the 20th term of the sequence.
-$$a _ { 1 } = - \frac { 3 } { 4 } , d = \frac { 5 } { 4 }$$
A) $a _ { n } = \frac { 5 } { 4 } n - 2 ; a _ { 20 } = 23$
B) $a _ { n } = \frac { 5 } { 4 } n - \frac { 3 } { 4 } ; a _ { 20 } = \frac { 97 } { 4 }$
C) $a _ { n } = - \frac { 3 } { 4 } n + \frac { 5 } { 4 } ; a _ { 20 } = - \frac { 55 } { 4 }$
D) $a _ { n } = - \frac { 3 } { 4 } n + 2 ; a _ { 20 } = - 13$

Question

Quizplus · Accepted Answer

The formula for the nth term of an arithmetic sequence is:$$a_n = a_1 + (n-1)d$$where $a_1$ is the first term, $d$ is the common difference, and $n$ is the term number.Substituting the given values into the formula, we get:$$a_n = -\frac{3}{4} + (n-1)\frac{5}{4}$$$$a_n = -\frac{3}{4} + \frac{5}{4}n - \frac{5}{4}$$$$a_n = \frac{5}{4}n - 2$$To find $a_{20}$, we substitute $n=20$ into the formula:$$a_{20} = \frac{5}{4}(20) - 2$$$$a_{20} = 25 - 2$$$$a_{20} = 23$$

Write a Formula for the General Term (The Nth Term) a1=−34,d=54a _ { 1 } = - \frac { 3 } { 4 } , d = \frac { 5 } { 4 }a1​=−43​,d=45​

Write a Formula for the General Term (The Nth Term) $a _ { 1 } = - \frac { 3 } { 4 } , d = \frac { 5 } { 4 }$