Asked by Chelsea Hennison on May 19, 2024
Verified
Write the first five terms of the sequence an=(−1) n+4n2+1a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }an=n2+1(−1) n+4 . Assume that n begins with 1.
A) a1=−12,a2=15,a3=−110,a4=117,a5=−126a _ { 1 } = - \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = - \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = - \frac { 1 } { 26 }a1=−21,a2=51,a3=−101,a4=171,a5=−261
B) a1=12,a2=15,a3=110,a4=117,a5=126a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }a1=21,a2=51,a3=101,a4=171,a5=261
C) a1=−1,a2=14,a3=−19,a4=116,a5=−125a _ { 1 } = - 1 , a _ { 2 } = \frac { 1 } { 4 } , a _ { 3 } = - \frac { 1 } { 9 } , a _ { 4 } = \frac { 1 } { 16 } , a _ { 5 } = - \frac { 1 } { 25 }a1=−1,a2=41,a3=−91,a4=161,a5=−251
D) a1=12,a2=−15,a3=110,a4=−117,a5=126a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = - \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = - \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }a1=21,a2=−51,a3=101,a4=−171,a5=261
E) a1=1,a2=−14,a3=19,a4=−116,a5=125a _ { 1 } = 1 , a _ { 2 } = - \frac { 1 } { 4 } , a _ { 3 } = \frac { 1 } { 9 } , a _ { 4 } = - \frac { 1 } { 16 } , a _ { 5 } = \frac { 1 } { 25 }a1=1,a2=−41,a3=91,a4=−161,a5=251
\(n ^ { 2 }\)
An algebraic expression indicating the square of the variable n.
\(( - 1 ) ^ { n + 4 }\)
An expression representing alternating positive and negative values for different integers n.
- Determine sequences derived from a provided formula.
- Pinpoint the opening five entries of a designated sequence.
Verified Answer
GO
Gaselle OrtizMay 24, 2024
Final Answer :
A
Explanation :
Plug in n = 1, 2, 3, 4, 5 to the expression of ana_nan given. We get −12,15,−110,117,−126-\frac{1}{2}, \frac{1}{5}, -\frac{1}{10}, \frac{1}{17}, -\frac{1}{26}−21,51,−101,171,−261 respectively. Therefore, the first five terms of the sequence are −12,15,−110,117,−126-\frac{1}{2}, \frac{1}{5}, -\frac{1}{10}, \frac{1}{17}, -\frac{1}{26}−21,51,−101,171,−261 . Thus choice A is correct.
Learning Objectives
- Determine sequences derived from a provided formula.
- Pinpoint the opening five entries of a designated sequence.