![]() Using the arithmetic sequence rule, we will get the following:Ī₁₅ = a₁ + f × (15-1) = 4 + 2 × 14 = 4 + 28 = 32 To solve the problem, we need to calculate the value of a₁₅ and compare it to the number of people – 40. Therefore, the last term of the sequence will be a₁₅. The situation above describes an arithmetic sequence with the common difference f = 2: a₁ = 4, a₂ = 6, a₃ = 8, … The restaurant only has 15 tables. Will there be enough tables to seat everyone at one big joint table? The restaurant only has 15 tables, and you are coming with a big group of 40 people. If you move two tables together, you can seat 6 people. Usually, in this restaurant, people sit at small square tables so that four people fit at each table. Imagine you want to organize a holiday dinner at a restaurant. Let's look at an example of using an arithmetic sequence in real life. The more accurate value of the golden ratio you will use, the closer the calculated value of an will be to the corresponding integer of the Fibonacci sequence. The golden ratio can also be used to find the terms of the Fibonacci sequence by using the following formula: The greater the terms of the sequence, the closer their ratio is to the golden ratio. This property means that the ratio of any two consecutive numbers (starting with a₃ and a₄) from the Fibonacci sequence is close to the golden ratio, approximately estimated as 1.618034, and denoted as ϕ. The Fibonacci sequence has many interesting properties, the most notable being the golden ratio property. Unlike other sequences, the Fibonacci sequence starts with a₀, not a₁! This means that a₀ = 0, a₁ = 1, a₂ = 1, a₃ = 2, and so on. The first two terms of a Fibonacci sequence are commonly defined as 0 and 1. In this sequence, each term is defined as the sum of two previous terms: A number sequence is denoted as a list of numbers separated by commas and enclosed in curly brackets. ![]() "In order" means that each number has a fixed position. In mathematics, a number sequence is defined as a list of numbers in order. Enter the value of n, and press "Calculate." The calculator will return the nᵗʰ term of the sequence and the sum of all numbers up to (and including) the nᵗʰ value. Use the Fibonacci sequence calculator to find the nᵗʰ term of the Fibonacci sequence. Then press "Calculate." The calculator will return the value of the nᵗʰ term of the sequence and the sum of all numbers up to (and including) the nᵗʰ term. ![]() Enter the first number of the sequence, the common ratio (usually denoted as r), and the value of n. Use the geometric sequence calculator to find the nᵗʰ term of the geometric sequence. The calculator will return the 20ᵗʰ value and the sum of all terms up to (and including) the 20ᵗʰ term. For example, if you need the twentieth term, enter n = 20. Then enter the value of n to obtain the nᵗʰ number of the sequence. Enter the first number of the sequence and the common difference (usually denoted as f). Use the arithmetic sequence calculator to find the nᵗʰ term of the arithmetic sequence. Directions for use Arithmetic sequence calculator In each case, the sequence calculator finds the nth term of the sequence. This number sequence calculator includes arithmetic, geometric, and Fibonacci or recursive sequence calculator.
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