Asked by Cinthia Balandran on Mar 10, 2024
Verified
Write an expression for the n th term of the sequence 16,−136,1216,−11296,…\frac { 1 } { 6 } , - \frac { 1 } { 36 } , \frac { 1 } { 216 } , - \frac { 1 } { 1296 } , \ldots61,−361,2161,−12961,… Assume that n begins with 1.
A) an=(−1) n6n+2a _ { n } = \frac { ( - 1 ) ^ { n } } { 6 ^ { n + 2 } }an=6n+2(−1) n
B) an=(−1) n+16n+1a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { 6 ^ { n + 1 } }an=6n+1(−1) n+1
C) an=(−1) n6n+1a _ { n } = \frac { ( - 1 ) ^ { n } } { 6 ^ { n + 1 } }an=6n+1(−1) n
D) an=(−1) n+16na _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { 6 ^ { n } }an=6n(−1) n+1
E) an=(−1) n6na _ { n } = \frac { ( - 1 ) ^ { n } } { 6 ^ { n } }an=6n(−1) n
\(6 ^ { n + 2 }\)
An exponential expression representing six raised to the power of n plus two, where n is any real number.
\(- 1\)
Represents a negative unit value in mathematics, often used to indicate the opposite or additive inverse of a positive value.
- Establish an expression for the nth term associated with a sequence pattern.
Verified Answer
NV
Nicholas VillapianoMar 10, 2024
Final Answer :
D
Explanation :
Looking at the sequence, notice that the denominators are powers of 6, indicating that the expression involves 6 raised to a power. Also, notice that the signs alternate between positive and negative, indicating the use of (-1)^n or (-1)^(n+1). Since the first term is positive, and the negative terms begin with the second term, we choose (-1)^(n+1) instead of (-1)^n. Finally, since the term is the reciprocal of the denominator, we end up with the expression (−1)n+16n\frac{( - 1 ) ^ { n + 1 }}{6^{n}}6n(−1)n+1 which matches choice D.
Learning Objectives
- Establish an expression for the nth term associated with a sequence pattern.