Search results
May 3, 2014 · The sum of 0 + ⋯ + n − 1 is 1 2(n − 1)n. Here n is the number of users; there are 0 comparisons needed for the first user alone, 1 for the second user (to compare them to the first), 2 for the third user, and so on, up to the n th user who must be compared with the n − 1 previous users.
Question. A sequence is defined by the recurrence relation \ ( {U_ {n + 1}} = 3 {U_n}\) and has \ ( {U_0} = 1\). a) Find the first five terms of the sequence. b) Determine the formula for \ (...
Jan 15, 2017 · Read How to Ask and include a minimal reproducible example. ahahah @EdHeal! But I think you forgot the \n s: #include <stdio.h> int main () { printf ("5 5 5 5 5\n4 4 4 4\n3 3 3\n2 2\n1"); } Give the full requirements for your task.
- Infinite Or Finite
- In Order
- Like A Set
- As A Formula
- Many Rules
- Notation
- Arithmetic Sequences
- Geometric Sequences
- Triangular Numbers
- Fibonacci Sequence
When the sequence goes on forever it is called an infinite sequence, otherwise it is a finite sequence
When we say the terms are "in order", we are free to define what order that is! They could go forwards, backwards ... or they could alternate ... or any type of order we want!
A Sequence is like a Set, except: 1. the terms are in order(with Sets the order does not matter) 2. the same value can appear many times (only once in Sets)
Saying "starts at 3 and jumps 2 every time" is fine, but it doesn't help us calculate the: 1. 10thterm, 2. 100thterm, or 3. nth term, where ncould be any term number we want.
But mathematics is so powerful we can find more than one Rulethat works for any sequence. So it is best to say "A Rule" rather than "The Rule" (unless we know it is the right Rule).
To make it easier to use rules, we often use this special style: So a rule for {3, 5, 7, 9, ...}can be written as an equation like this: xn= 2n+1 And to calculate the 10th term we can write: x10 = 2n+1 = 2×10+1 = 21 Can you calculate x50(the 50th term) doing this? Here is another example:
In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add some value each time ... on to infinity. In Generalwe can write an arithmetic sequence like this: {a, a+d, a+2d, a+3d, ... } where: 1. ais the first term, and 2. d is the difference between the terms (called the "common difference") And...
In a Geometric Sequence each term is found by multiplying the previous term by a constant. In Generalwe can write a geometric sequence like this: {a, ar, ar2, ar3, ... } where: 1. ais the first term, and 2. r is the factor between the terms (called the "common ratio") And the rule is: xn = ar(n-1) (We use "n-1" because ar0is the 1st term)
The Triangular Number Sequenceis generated from a pattern of dots which form a triangle: By adding another row of dots and counting all the dots we can find the next number of the sequence.
The next number is found by adding the two numbers before ittogether: 1. The 2 is found by adding the two numbers before it (1+1) 2. The 21 is found by adding the two numbers before it (8+13) 3. etc... Rule is xn = xn-1 + xn-2 That rule is interesting because it depends on the values of the previous two terms. The Fibonacci Sequence is numbered fro...
For each of the following relations \sim on \mathbb {R}\times\mathbb {R}, determine whether it is an equivalence relation. For those that are, describe geometrically the equivalence class [ (a,b)]. (x_1,y_1)\sim (x_2,y_2) \,\Leftrightarrow\, x_1+y_2=x_2+y_1.
Examples. \left. \begin {cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end {cases} \right. Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more.
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.
