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Solved: List the first 10 terms of each of these
Chapter 1, Problem 6E(choose chapter or problem)
List the first 10 terms of each of these sequences.a) the sequence obtained by starting with 10 and obtaining each term by subtracting 3 from the previous term________________b) the sequence whose nth term is the sum of the first n positive integers________________c) the sequence whose nth term is ________________d) the sequence whose nth term is ________________e) the sequence whose first two terms are 1 and 5 and each succeeding term is the sum of the two previous terms________________f) the sequence whose nth term is the largest integer whose binary expansion (defined in Section 4.2) has n bits (Write your answer in decimal notation.)________________g) the sequence whose terms are constructed sequentially as follows: start with 1, then add 1, then multiply by 1, then add 2, then multiply by 2, and so on________________h) the sequence whose nth term is the largest integer k such that k! ? n
Questions & Answers
QUESTION:
List the first 10 terms of each of these sequences.a) the sequence obtained by starting with 10 and obtaining each term by subtracting 3 from the previous term________________b) the sequence whose nth term is the sum of the first n positive integers________________c) the sequence whose nth term is ________________d) the sequence whose nth term is ________________e) the sequence whose first two terms are 1 and 5 and each succeeding term is the sum of the two previous terms________________f) the sequence whose nth term is the largest integer whose binary expansion (defined in Section 4.2) has n bits (Write your answer in decimal notation.)________________g) the sequence whose terms are constructed sequentially as follows: start with 1, then add 1, then multiply by 1, then add 2, then multiply by 2, and so on________________h) the sequence whose nth term is the largest integer k such that k! ? n
ANSWER:SolutionStep-1: In this problem we need to find the first 10 terms of the sequences.a)Given first term of the sequence is ten. That is , . Consider , the term of the sequence , since each term by subtracting 3 from the previous term . If n = 2, then . If n = 3, then . If n = 4, then . If n = 5, then . If n = 6, then . If n = 7, then . If n = 8, then . If n = 9, then . If n = 10, then . Therefore , the first ten terms of the sequence is 10 , 7,4, 1, -2 , -5 , -8 , -11, -14 and -17.Step-2:b)term = sum of the first n positive integers. = 1+2+3+.....+n That is , .If n =1 , then .If n =2 , then .If n =3 , then .If n =4 , then .If n =5 , then .If n =6 , then .If n =7 , then .If n =8 , then .If n = 9, then .If n =10 , then .Therefore , the first 10 terms of the sequence is : 1 , 3, 6, 10 , 15 , 21, 28 , 36 , 45 and 55.Step-3:c) te