Asked by Dusty Taylor on May 16, 2024
Verified
Write an expression for the n th term of the sequence 4,42,46,424,4120,…4 , \frac { 4 } { 2 } , \frac { 4 } { 6 } , \frac { 4 } { 24 } , \frac { 4 } { 120 } , \ldots4,24,64,244,1204,… Assume that n begins with 1.
A) an=4+1n!a _ { n } = 4 + \frac { 1 } { n ! }an=4+n!1
B) an=4(n+1) a _ { n } = \frac { 4 } { ( n + 1 ) }an=(n+1) 4
C) an=4n(n+1) a _ { n } = \frac { 4 } { n ( n + 1 ) }an=n(n+1) 4
D) an=4n!a _ { n } = \frac { 4 } { n ! }an=n!4
E) an=4+1(n+1) !a _ { n } = 4 + \frac { 1 } { ( n + 1 ) ! }an=4+(n+1) !1
\(n !\)
\(n !\), pronounced n factorial, is the product of all positive integers less than or equal to n. For instance, \(4! = 4 \times 3 \times 2 \times 1 = 24\).
- Derive an expression for the nth term derived from a sequence pattern.
Verified Answer
NV
Nikolas VellingerMay 23, 2024
Final Answer :
D
Explanation :
The given sequence is 4,42,46,424,4120,…4, \frac{4}{2}, \frac{4}{6}, \frac{4}{24}, \frac{4}{120}, \ldots4,24,64,244,1204,… , where the denominator follows the pattern of factorial numbers starting from 1!1!1! for n=1n=1n=1 . Thus, the nnn th term is given by an=4n!a_n = \frac{4}{n!}an=n!4 .
Learning Objectives
- Derive an expression for the nth term derived from a sequence pattern.