in Set Theory & Algebra edited by
3,232 views
1 vote
1 vote

List the first $10$ terms of each of these sequences.

  1. the sequence obtained by starting with $10$ and obtaining each term by subtracting $3$ from the previous term
  2. the sequence whose nth term is the sum of the first $n$ positive integers
  3. the sequence whose $nth$ term is $3^{n} − 2^{n}$
  4. the sequence whose $nth$ term is $\left \lfloor \sqrt{n} \right \rfloor$
  5. the sequence whose first two terms are $1$ and $5$ and each succeeding term is the sum of the two previous terms
  6. 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.)
  7. 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
  8. the sequence whose nth term is the largest integer $k$ such that $k! \leq n$
in Set Theory & Algebra edited by
by
3.2k views

1 Answer

0 votes
0 votes
A).$10,7,4,1,-2,-5,-8,-11,-14,-17$

B).$1,3,6,10,15,21,28,36,45,55$

C).$0,1,5,19,65,211,665,2059,6305,19171,58025$

D).$\sqrt{1},\sqrt{2},\sqrt{3},\sqrt{4},\sqrt{5},\sqrt{6},\sqrt{7},\sqrt{8},\sqrt{9},\sqrt{10}$

E).$1,5,6,11,17,28,45,73,118,191$

F).$1,3,7,15,31,63,127,254,511,1023$

G).$1,2,2,4,8,11,33,37,148,153$

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true