Asked by Neisha Bethly on Jun 07, 2024
Verified
Write the first five terms of the sequence an=−4−13na _ { n } = - 4 - \frac { 1 } { 3 ^ { n } }an=−4−3n1 . Assume that n begins with 1.
A) a1=−113,a2=−359,a3=−10727,a4=−32381,a5=−971243a _ { 1 } = - \frac { 11 } { 3 } , a _ { 2 } = - \frac { 35 } { 9 } , a _ { 3 } = - \frac { 107 } { 27 } , a _ { 4 } = - \frac { 323 } { 81 } , a _ { 5 } = - \frac { 971 } { 243 }a1=−311,a2=−935,a3=−27107,a4=−81323,a5=−243971
B) a1=−133,a2=−379,a3=−10927,a4=−32581,a5=−973243a _ { 1 } = - \frac { 13 } { 3 } , a _ { 2 } = - \frac { 37 } { 9 } , a _ { 3 } = - \frac { 109 } { 27 } , a _ { 4 } = - \frac { 325 } { 81 } , a _ { 5 } = - \frac { 973 } { 243 }a1=−313,a2=−937,a3=−27109,a4=−81325,a5=−243973
C) a1=113,a2=359,a3=10727,a4=32381,a5=971243a _ { 1 } = \frac { 11 } { 3 } , a _ { 2 } = \frac { 35 } { 9 } , a _ { 3 } = \frac { 107 } { 27 } , a _ { 4 } = \frac { 323 } { 81 } , a _ { 5 } = \frac { 971 } { 243 }a1=311,a2=935,a3=27107,a4=81323,a5=243971
D) a1=−3,a2=113,a3=359,a4=10727,a5=32381a _ { 1 } = - 3 , a _ { 2 } = \frac { 11 } { 3 } , a _ { 3 } = \frac { 35 } { 9 } , a _ { 4 } = \frac { 107 } { 27 } , a _ { 5 } = \frac { 323 } { 81 }a1=−3,a2=311,a3=935,a4=27107,a5=81323
E) a1=−5,a2=−133,a3=−379,a4=−10927,a5=−32581a _ { 1 } = - 5 , a _ { 2 } = - \frac { 13 } { 3 } , a _ { 3 } = - \frac { 37 } { 9 } , a _ { 4 } = - \frac { 109 } { 27 } , a _ { 5 } = - \frac { 325 } { 81 }a1=−5,a2=−313,a3=−937,a4=−27109,a5=−81325
\(- 4\)
A negative integer, four units less than zero.
\(3 ^ { n }\)
An exponential expression where 3 is the base and \(n\) is the exponent, indicating three raised to the power of \(n\).
- Delineate the first quintet of terms in an identified sequence.
Verified Answer
LP
Lindsey PerryJun 10, 2024
Final Answer :
B
Explanation :
Substitute n = 1, 2, 3, 4, and 5 one by one in the given expression of the sequence to get;
a1 = -4 - 1/3^1 = -13/3
a2 = -4 - 1/3^2 = -37/9
a3 = -4 - 1/3^3 = -109/27
a4 = -4 - 1/3^4 = -325/81
a5 = -4 - 1/3^5 = -973/243
Therefore, the correct option is (B).
a1 = -4 - 1/3^1 = -13/3
a2 = -4 - 1/3^2 = -37/9
a3 = -4 - 1/3^3 = -109/27
a4 = -4 - 1/3^4 = -325/81
a5 = -4 - 1/3^5 = -973/243
Therefore, the correct option is (B).
Learning Objectives
- Delineate the first quintet of terms in an identified sequence.