Step 4: Solve for the explicit formula using the recursive formula and initial conditions: We know that a1 = 2, so we can substitute that into the recursive formula: an = 3an-1 – 2 a1 = 2 a2 = 3(a1) – 2 = 3(2) – 2 = 4 a3 = 3(a2) – 2 = 3(4) – 2 = 10 a4 = 3(a3) – 2 = 3(10) – 2 = 28įrom this, we can see that the explicit formula is: an = 3^n-1 * 2 Step 3: Express the nth term in terms of the previous terms: an = 3an-1 – 2 Step 2: Look for a pattern: We can see that the nth term is equal to 3 times the (n-1)th term minus 2. If the explicit formula does not match the initial terms, try to find a new pattern or check for errors in the previous steps.Įxample: Find the general formula for the recursive sequence defined by the following:.Test the explicit formula using the first few terms of the sequence to confirm it is correct.Solve for the explicit formula using the recursive formula found in step 3 and the initial conditions of the sequence.Use the pattern identified in step 2 to express the nth term of the sequence in terms of the previous terms.Attempt to find a pattern in the terms, such as a specific difference or ratio between consecutive terms.Start by identifying the first few terms of the recursive sequence.To find the general formula for the recursive sequence, follow the step-by-step guide below: Step-by-step to find the general formula for the recursive sequence \(a_n = f(a_)\) is called the return relation and describes the relationship in the sequence. The formula of a recursive sequence is as follows: + Ratio, Proportion & Percentages Puzzles.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |