Summary
Highlights
The video introduces a number sequence (e.g., 2000, 2160, 2320, 2480...) where each subsequent number increases by 160. The ellipsis (...) indicates that the sequence continues indefinitely.
A number in a sequence is called a 'term'. The first term is denoted as u0 (2000 in this example), followed by u1, u2, u3, and so on. In general, Un represents any arbitrary term, and Un-1 represents the term immediately before Un. The term u0 is also called the 'initial term'.
To create a recursive formula, we start with Un. To find Un, we take the preceding term, Un-1, and add 160. So the formula is Un = Un-1 + 160. It is crucial to also state the initial term with the formula, in this case, u0 = 2000, otherwise, no term can be calculated.
Given the recursive formula Un = 1.25 * Un-1 - 10 and u0 = 100, the task is to calculate the fifth term (u4). A recursive formula requires knowing the previous term. To calculate u4, you need u3, which requires u2, and so on, back to u0.
To calculate terms using a calculator, first input the initial term (100) and press enter. Then, input the formula using 'Ans' for the previous answer (1.25 * Ans - 10). Pressing enter repeatedly will yield u1, u2, u3, and so on. For u4, the result is 186.48.
The next task is to determine from which term Un becomes greater than 500. Using the same calculator method, repeatedly press enter until the value exceeds 500. It is important to note the term just before and the term where it first exceeds the value. In this case, u9 is 487.00, and u10 is 598.79. Therefore, from the 11th term (u10), Un is greater than 500.