// StartMathJax Script window.MathJax = {loader: {load: [ 'input/asciimath', 'ui/lazy', 'output/chtml', 'ui/menu']} }; (function() { var script = document.createElement('script'); script.src = "https://cdn.jsdelivr.net/npm/mathjax@3/es5/startup.js"; script.async = true; document.head.appendChild(script); })(); ---------- (Different files) ---------- // UpdateTypeset Script config = { attributes: true, childList: true, subtree: true }; // Callback function to execute when mutations are observed callback = (mutationList, observer) => { for (mutation of mutationList) { if (mutation.type === 'childList') { console.log('A child node has been added or removed.'); MathJax.typeset(); } else if (mutation.type === 'attributes') { console.log(The \${mutation.attributeName} attribute was modified.); } } }; // Create an observer instance linked to the callback function observer = new MutationObserver(callback); document.onreadystatechange = () => { if (document.readyState === 'complete') { console.log("Loaded fully according to readyState") targetNode = document.getElementById('content-wrapper') console.log(targetNode) // Start observing the target node for configured mutations observer.observe(targetNode, config); } }

Search

Updated: 6 days ago

There are several ways to find the equation for a quadratic sequence - I have found the following to be the best.

If we substitute the first term (1) into the general form, we get…

Which simplifies to…

This is shown in the table below immediately beneath the term’s value.

Here we have a sequence of numbers. I have included the differences between the numbers in the sequence.

Notice that the 2nd difference is constant across the sequence- a sure sign that you have a quadratic sequence.

Finding the next number in the sequence is easy - add the 1st and second differences together from n=4 to n=5 (58 + 8 = 66) then add this to the value for n=5 (207 + 66 = 273). The value for n=6 is 273.

Let's find out the quadratic equation that gave this sequence of numbers...

From the derived equations in the first table, we can calculate the values for a, b and c.

Sequence = a + b + c = 23

1st difference = 3a + b = 34

2nd difference = 2a = 8