![]() ![]() Recall that a sequence is just a list of numbers. ![]() Top answer: To find the second term of the sequence, we can substitute n 2 into the recursive formula. In this explainer, we will learn how to find the recursive formula of a sequence. Given the recursive formula for the geometric sequence a15, an25an1, find the second term of the sequence. Thankfully, you can convert an iterative formula to an explicit formula for arithmetic sequences. You can ask a new question or answer this question. 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. Here, we observe that the ratios 50/25010/502/10 are all 1/5. The recursive formula of the geometric sequence is given by option D an (1) × (5)(n - 1) for n 1 How to determine recursive formula of a geometric sequen See what teachers have to say about Brainlys new learning tools WATCH. 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 Recursive formula is ana(n-1)xx1/5 In a Geometric sequence, the ratio of each term to its preceding term is always constant and is known as common ratio r. nth term of Geometric Progression an an 1 × r for n 2. They are, nth term of Arithmetic Progression an an 1 + d for n 2. There are few recursive formulas to find the nth term based on the pattern of the given data. Substitute a and b into 2=a+b+c: 2=1+0+c, c=1 We explain the difference between both geometric sequence equations, the explicit and recursive formula for a geometric sequence, and how to use the geometric sequence formula with some interesting geometric sequence examples. Pattern rule to get any term from its previous terms. Then subtract the 2 equations just produced: Solve this using any method, but i'll use elimination: This will also show how to write a sequence given the. The function is y=ax^2+bx+c, so plug in each point to solve for a, b, and c. This video will show the step by step method in writing the recursive formula of a geometric sequence. 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. Use an explicit formula for a geometric sequence. However, you might notice that the differences of the differences between the numbers are equal (5-3=2, 7-5=2). Use a recursive formula for a geometric sequence. 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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