Since the question was originally only asking for the value of the third term we know our solution only needs to be the value of the third term which is 9. Step 5: We found the recursive sequence we were looking for: 1,3,9. Thankfully, you can convert an iterative formula to an explicit formula for arithmetic sequences. This recursive formula is a geometric sequence. In the explicit formula "d(n-1)" means "the common difference times (n-1), where n is the integer ID of term's location in the sequence." In the iterative formula, "a(n-1)" means "the value of the (n-1)th term in the sequence", this is not "a times (n-1)." Even though they both find the same thing, they each work differently-they're NOT the same form. A + B(n-1) is the standard form because it gives us two useful pieces of information without needing to manipulate the formula (the starting term A, and the common difference B).Īn explicit formula isn't another name for an iterative formula. M + Bn and A + B(n-1) are both equivalent explicit formulas for arithmetic sequences. So the equation becomes y=1x^2+0x+1, or y=x^2+1ītw you can check (4,17) to make sure it's right Substitute a and b into 2=a+b+c: 2=1+0+c, c=1 Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. Then subtract the 2 equations just produced: Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Solve this using any method, but i'll use elimination: The function is y=ax^2+bx+c, so plug in each point to solve for a, b, and c. Let x=the position of the term in the sequence Since the sequence is quadratic, you only need 3 terms. that means the sequence is quadratic/power of 2. However, you might notice that the differences of the differences between the numbers are equal (5-3=2, 7-5=2). This work is licensed under a Creative Commons Attribution 4.0 License.This isn't an arithmetic ("linear") sequence because the differences between the numbers are different (5-2=3, 10-5=5, 17-10=7) It is, however, most common to divide the second term by the first term because it is often the easiest method of finding the common ratio. We can divide any term in the sequence by the previous term. The common ratio is also the base of an exponential function as shown in Figure 2ĭo we have to divide the second term by the first term to find the common ratio? The sequence of data points follows an exponential pattern. Substitute the common ratio into the recursive formula for geometric sequences and define. Create a recursive formula by stating the first term, and then stating the formula to be the previous term plus the common difference. The common ratio can be found by dividing the second term by the first term. Write a recursive formula for the following geometric sequence.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |