Kenneth Rosen Edition 7 Exercise 2.4 Question 5 (Page No. 167)

Question

List the first $10$ terms of each of these sequences.

• A. the sequence that begins with $2$ and in which each successive term is $3$ more than the preceding term
• B. the sequence that lists each positive integer three times, in increasing order
• C. the sequence that lists the odd positive integers in increasing order, listing each odd integer twice
• D. the sequence whose $nth$ term is $n! − 2^{n}$
• E. the sequence that begins with $3,$ where each succeeding term is twice the preceding term
• F. the sequence whose first term is $2,$ second term is $4,$ and each succeeding term is the sum of the two preceding terms
• G. the sequence whose $nth$ term is the number of bits in the binary expansion of the number $n$ (defined in Section $4.2$)
• H. the sequence where the $nth$ term is the number of letters in the English word for the index $n$

Answer 1

A),$2,5,8,11,14,17,20,23,26,29$

B).$1,3,9,27,81,243,729,2187,6561,19683$

C).$1,1,3,3,5,5,7,7,9,9$

D).$0,-1,-2,-2,8,88,656,4912,40064,362368$

E).$3,6,12,24,48,96,192,384,768,1536$

F).$2,4,6,10,16,26,42,68,110,178$

G).$2,4,8,16,32,64,128,256,512,1024$

H).$A,AB,ABC,ABCD,ABCDE,ABCDEF,ABCDEFG,ABCDEFGH,ABCDEFGHI,ABCDEFGHIJ$