Download Gretel Amman CS 242 Homework 3 – Problem 15 Page 161 #10 10

Gretel Amman
CS 242
Homework 3 – Problem 15
Page 161 #10
10. For each of these lists of integers, provide a simple formula or rule that generates the
terms of an integer sequence that begins with the given list. Assuming that your formula is
correct, determine the next three terms of the sequence.
a) 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, . . .
The pattern is an = n2 + 2. The next three terms are 123, 146, 171.
b) 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, . . .
The pattern is an = 4n + 3. The next three terms are 47, 51, 55.
c) 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .
The pattern is going through all binary strings in order. It is the sequence of natural numbers
written in binary form. The next three terms are 1100, 1101, 1110.
d) 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, . . .
The pattern is made up of Fibonacci numbers starting with one 1, the three 2’s, then five 3’s,
and so on. The number of copies increase by two each time. The next three terms are 8, 8, 8.
e) 0, 2, 8, 26, 80, 242, 728, 2186, 6560, 19682, . . .
The pattern is an = 3n-1 - 1. The next three terms are 59048, 177146, 531440.
f) 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .
The pattern is starting with 1, you multiply it by 3 to get 3, and then multiply 3 by 5 to get 15,
and then multiply 15 by 7 to get 105, and so on. You continue multiplying the product by the
next consecutive odd number. The next three terms are 654729075, 13749310575,
316234143225.
g) 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, . . .
The pattern is on 1, two 0’s, three 1’s, four 0’s and so on. 1’s and 0’s are alternating and the
amount of these two numbers is increasing by one each time. The next three terms are 0, 0, 0.
h) 2, 4, 16, 256, 65536, 4294967296, . . .
The pattern is starting with 2, the next term is the square of the previous term. 2 2 = 4, so then
you take 4 and square it to get 16, and then you take 16 and square it to get 256, and so on.
The next three terms are 18446744073709551616,
340282366920938463463374607431768211456,
1157920892373161954235709850086879078532699846656405640394575840079131296399
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