Write the first five terms of the sequence defined recursively. Use the pattern to write the nth term of the sequence as a function of n. (Assume that n begins with 1.)
a (small) 1 =4,a (small) (k+1) =−a (small) k
a. a (small) n =4(−1)^n−1
b. a (small) n =4n
c. a (small) n =(−4)^n−1
d. a (small) n =(−4)^n
e. a (small) n =4(−1)^n
+118608 Write the first five terms of the sequence defined recursively. Use the pattern to write the nth term of the sequence as a function of n. (Assume that n begins with 1.)
a (small) 1 =4,a (small) (k+1) =−a (small) k
\(a_1=4, \qquad a_{k+1}=-a_k\\~\\ a_1=4\\ a_2=-a_1=-4\\ a_3=-a_2=+4\\ a_4=-4 \qquad =4*- 1 = 4*(-1)^3 \\ a_5=+4 \qquad =4* -1=4*(-1)^4\\~\\ a^n= 4*(-1)^{n-1} \)
a. a (small) n =4(−1)^n−1
b. a (small) n =4n
c. a (small) n =(−4)^n−1
d. a (small) n =(−4)^n
e. a (small) n =4(−1)^n
