Answer to Question #271599 in Discrete Mathematics for Jaishree

Question #271599

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 in-



creasing order, listing each odd integer twice



d) the sequence whose nth term is n! − 2n



e) the sequence that begins with 3, where each succeed-



ing 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 pre-



ceding 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 let-



ters in the English word for the index n

1
Expert's answer
2021-11-26T13:10:00-0500

a)

2,5,8,11,14,17,20,23,26,292,5,8,11,14,17,20,23,26,29

b)


1,1,1,2,2,2,3,3,3,41,1,1,2,2,2,3,3,3,4

c)


1,1,3,3,5,5,7,7,9,91,1,3,3,5,5,7,7,9,9

d)


a1=1!2(1)=1a_1=1!-2(1)=-1

a2=2!2(2)=2a_2=2!-2(2)=-2

a3=3!2(3)=0a_3=3!-2(3)=0

a4=4!2(4)=16a_4=4!-2(4)=16

a5=5!2(5)=110a_5=5!-2(5)=110

a6=6!2(6)=708a_6=6!-2(6)=708

a7=7!2(7)=5026a_7=7!-2(7)=5026

a8=8!2(8)=40304a_8=8!-2(8)=40304

a9=9!2(9)=362862a_9=9!-2(9)=362862

a10=10!2(10)=3628780a_{10}=10!-2(10)=3628780


1,2,0,16,110,708,5026,40304,362862,3628780-1,-2,0, 16, 110, 708, 5026,40304,362862,3628780

e)


3,6,12,24,48,96,192,384,768,15363,6,12,24,48,96,192,384,768,1536

f)


2,4,6,10,16,26,42,68,110,1782,4,6,10,16,26,42,68,110,178

g)


2,4,8,16,32,64,128,256,512,10242,4,8,16,32,64,128,256,512,1024

h)


A,AB,ABC,ABCD,ABCDE,A,AB,ABC,ABCD,ABCDE,

ABCDEF,ABCDEFG,ABCDEFGH,ABCDEF,ABCDEFG,ABCDEFGH,

ABCDEFGHI,ABCDEFGHIJABCDEFGHI,ABCDEFGHIJ


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