During the first second, it travels four meters down. We will take a close look at the example of free fall.Ī stone is falling freely down a deep shaft. Let's analyze a simple example that can be solved using the arithmetic sequence formula. This formula will allow you to find the sum of an arithmetic sequence. Substituting the arithmetic sequence equation for nᵗʰ term: All you have to do is to add the first and last term of the sequence and multiply that sum by the number of pairs (i.e., by n/2). That means that we don't have to add all numbers. The sum of each pair is constant and equal to 24. We will add the first and last term together, then the second and second-to-last, third and third-to-last, etc. Let's try to sum the terms in a more organized fashion. We could sum all of the terms by hand, but it is not necessary. Look at the first example of an arithmetic sequence: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. Trust us, you can do it by yourself - it's not that hard! Our arithmetic sequence calculator can also find the sum of the sequence (called the arithmetic series) for you. A perfect spiral - just like this one! (Credit: Wikimedia.) If you drew squares with sides of length equal to the consecutive terms of this sequence, you'd obtain a perfect spiral. Each term is found by adding up the two terms before it.Ī great application of the Fibonacci sequence is constructing a spiral. This is not an example of an arithmetic sequence, but a special case called the Fibonacci sequence. Now, let's take a close look at this sequence:Ĭan you deduce what is the common difference in this case? What happens in the case of zero difference? Well, you will obtain a monotone sequence, where each term is equal to the previous one. Naturally, if the difference is negative, the sequence will be decreasing. If the common difference of an arithmetic sequence is positive, we call it an increasing sequence. In fact, it doesn't even have to be positive! You do the same thing (multiply, divide add or subtract) to bothīy doing the same thing to both sides of the equation you can find what one x is equal to.Some examples of an arithmetic sequence include:Ĭan you find the common difference of each of these sequences? Hint: try subtracting a term from the following term.īased on these examples of arithmetic sequences, you can observe that the common difference doesn't need to be a natural number - it could be a fraction. The equation will remain balanced only if Way to solve equations by thinking of the two sides of the equationĪs two sides of a balance. This button restarts the difficulty level but will present different equations. A Restart button is provided if the questions generated start to become a little too difficult.
It is not possible to predict how quickly you will develop confidence solving equations of a particular type but typically the examples will increase in difficulty very slightly each time you press the Next button. You canĬhange the options so that one of five different types of equation Make up unlimited equations for you to practise solving. To find which value is represented by the letter x. There will be no powers (squared, cubed etc). In simple terms it is a mathematical sentence in which youĬan see only one letter (which might appear more than once) but A linear equation is an equation in which each term is either aĬonstant or the product of a constant times the first power of a
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