Answer to Question #271599 in Discrete Mathematics for Jaishree

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 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

Answer 1

a)

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

b)

$$1,1,1,2,2,2,3,3,3,4$$

c)

$$1,1,3,3,5,5,7,7,9,9$$

d)

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

$$a_2=2!-2(2)=-2$$

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

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

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

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

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

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

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

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

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

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)

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

$$ABCDEF,ABCDEFG,ABCDEFGH,$$

$$ABCDEFGHI,ABCDEFGHIJ$$