$\text { Write an expression for the } n \text {th term of the sequence } \frac { 10 } { 11 } , \frac { 19 } { 20 } , \frac { 28 } { 29 } , \frac { 37 } { 38 } , \ldots$
A) $\frac { 9 n } { 9 n + 2 }$
B) $\frac { 9 n } { 9 n + 1 }$
C) $\frac { 9 n - 1 } { 9 n + 1 }$
D) $\frac { 9 n + 1 } { 9 n + 2 }$
E) $\frac { 9 n - 1 } { 9 n + 2 }$

Question

$\text { Write an expression for the } n \text {th term of the sequence } \frac { 10 } { 11 } , \frac { 19 } { 20 } , \frac { 28 } { 29 } , \frac { 37 } { 38 } , \ldots$ 
A) $\frac { 9 n } { 9 n + 2 }$
B) $\frac { 9 n } { 9 n + 1 }$
C) $\frac { 9 n - 1 } { 9 n + 1 }$
D) $\frac { 9 n + 1 } { 9 n + 2 }$
E) $\frac { 9 n - 1 } { 9 n + 2 }$

Quizplus · Accepted Answer

The numerator increases by 9 for each term (10, 19, 28, 37, ...), which can be represented as $9n + 1$ for the nth term (where n starts from 0). The denominator is always 1 more than the numerator, which gives $9n + 2$ for the denominator. Thus, the nth term is $\frac { 9 n + 1 } { 9 n + 2 }$.

A) 9n9n+2\frac { 9 n } { 9 n + 2 }9n+29n​

A) $\frac { 9 n } { 9 n + 2 }$