Given the sequence $4 + \frac { 7 } { 8 } , 4 + \frac { 8 } { 9 } , 4 + \frac { 9 } { 10 } , 4 + \frac { 10 } { 11 } , 4 + \frac { 11 } { 12 } , \ldots$, write an expression for the apparent $n$th term assuming $n$ begins with 1 .
A) $\frac { 6 n + 34 } { n + 7 }$
B) $\frac { 5 n + 35 } { n + 7 }$
C) $\frac { 5 n + 34 } { n + 7 }$
D) $\frac { 5 n + 34 } { n + 8 }$
E) $\frac { 6 n + 35 } { n + 8 }$

Question

Quizplus · Accepted Answer

The sequence can be written as $4 + \frac{n+6}{n+7}$ for the $n$th term, starting with $n=1$. Simplifying this expression gives $\frac{4(n+7) + n+6}{n+7} = \frac{5n + 34}{n+7}$, which matches option C.

Given the Sequence 4+78,4+89,4+910,4+1011,4+1112,…4 + \frac { 7 } { 8 } , 4 + \frac { 8 } { 9 } , 4 + \frac { 9 } { 10 } , 4 + \frac { 10 } { 11 } , 4 + \frac { 11 } { 12 } , \ldots4+87​,4+98​,4+109​,4+1110​,4+1211​,…

Given the Sequence $4 + \frac { 7 } { 8 } , 4 + \frac { 8 } { 9 } , 4 + \frac { 9 } { 10 } , 4 + \frac { 10 } { 11 } , 4 + \frac { 11 } { 12 } , \ldots$