![]() ![]() Thankfully, you can convert an iterative formula to an explicit formula for arithmetic sequences. 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)." Actually the explicit formula for an arithmetic sequence is a (n)a+ (n-1)D, and the recursive formula is a (n) a (n-1) + D (instead of a (n)a+D (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. The difference is than an explicit Arithmetic Sequence Calculator on the App Store - Apple. 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 Explicit formulas for arithmetic sequences. Substitute a and b into 2=a+b+c: 2=1+0+c, c=1 Then subtract the 2 equations just produced: 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 isn't an arithmetic ("linear") sequence because the differences between the numbers are different (5-2=3, 10-5=5, 17-10=7)
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