Asked by Bijeta Pradhan on Jul 15, 2024
Verified
Write an expression for the n th term of the sequence 89,910,1011,1112,1213,....\frac { 8 } { 9 } , \frac { 9 } { 10 } , \frac { 10 } { 11 } , \frac { 11 } { 12 } , \frac { 12 } { 13 } ,....98,109,1110,1211,1312,.... Assume that n begins with 1.
A) an=n+7n+8a _ { n } = \frac { n + 7 } { n + 8 }an=n+8n+7
B) an=n+8n+9a _ { n } = \frac { n + 8 } { n + 9 }an=n+9n+8
C) an=(n+8) !(n+9) !a _ { n } = \frac { ( n + 8 ) ! } { ( n + 9 ) ! }an=(n+9) !(n+8) !
D) an=n+9n+10a _ { n } = \frac { n + 9 } { n + 10 }an=n+10n+9
E) an=(n+7) !(n+8) !a _ { n } = \frac { ( n + 7 ) ! } { ( n + 8 ) ! }an=(n+8) !(n+7) !
\(n + 7\)
An algebraic expression representing the sum of an unknown quantity \(n\) and the number 7.
\(n + 8\)
An algebraic expression representing the sum of a variable n and the number 8.
- Formulate an expression for the nth term originating from a sequence pattern.
Verified Answer
DS
Daniel Salas MoraJul 18, 2024
Final Answer :
A
Explanation :
The numerator of each fraction increases by 1 starting from 8, and the denominator increases by 1 starting from 9, which matches the pattern of an=n+7n+8a_n = \frac{n + 7}{n + 8}an=n+8n+7 when substituting n = 1, 2, 3, etc.
Learning Objectives
- Formulate an expression for the nth term originating from a sequence pattern.