We can display this in a recursive formula using the following: an = (an-1)(2) where a1=3 an = term number and an-1 = the term before the n termħ Use recursive formulas for arithmetic sequences:įind the 5th term: an = an-1 + 2 2, 4, 6, … We know the 3rd term in this sequence is 6 and it is arithmetic with d=2. an = (an-1)(-0.5) Means geometric with r=-.5 so take the prior term and just multiply by -.5 to find the next Means take the previous term and multiply by r to continue the patternĦ Write recursive formulas for geometric SequencesĮXAMPLE: Write the recursive formula for the sequence: 3, 6, 12, 24… A recursive formula tells us how each term is connected to the next term It is geometric and the ratio between each term is 2. We can display this in a recursive formula using the following: an = an where a1=2 an = term number and an-1 = the term before the n termĥ Write recursive formulas for geometric SequencesĮx. an = an-1 + 7 Means arithmetic with d=7, so take the prior term and just add 7 to find the next Means take the previous term and add the d to continue the pattern The rules for recursive formulas may look more complicated, but are actually very logical (and often easier to use than explicit).Ĥ Write recursive formulas for Arithmetic SequencesĮXAMPLE: Write the recursive formula for the sequence: 2, 4, 6, 8… A recursive formula tells us how each term is connected to the next term It is arithmetic and the difference between each term is 2.

They will have an an-1 somewhere in the equation which represents the term prior to the term you are solving for, and they will give you a specific valueģ Write recursive formulas for Arithmetic SequencesĮx. You have to know what came before it Recursive formulas can be used for arithmetic or geometric sequences Recursive formulas look a little different than explicit. A recursive formula always uses the preceding term to define the next term of the sequence. 2 Recursive formula A Recursive Formula is a formula that calculates each term of a sequence based on the preceding term (term that came right before).

Formula for recursive sequence