Chapter 2: Q5E (page 167)
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 listseach 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\({n^{th}}\) term is \(n! - {2^n}\)
e. Thesequence that begins with 3, where each succeeding term is twice the preceding term.
f. Thesequence 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\({n^{th}}\)term is the number of bits in the binary expansion of the number n (defined in section 4.2).
h. The sequence where the\({n^{th}}\)term is the number of letters in the English word for the index n.
Short Answer
Hence, the terms of the given sequence are:
\(\begin{array}{l}a){\rm{ }}2,5,8,11,14,17,20,23,26,29\\b){\rm{ }}1,1,1,2,2,2,3,3,3,4\\c){\rm{ }}1,1,3,3,5,5,7,7,9,9\\d) - 1, - 2, - 2,8,88,656,4912,40064,362368,3627776\\e){\rm{ }}3,6,12,24,48,96,192,384,768,1536\\f){\rm{ }}2,4,6,10,16,26,42,68,110,178\\g){\rm{ }}1,2,2,3,3,3,3,4,4,4\\h){\rm{ }}3,3,5,4,4,3,5,5,4,3\end{array}\)