![]() Likewise, we can find the values of any term in the sequence. In explicit formulas, we can find the value of a specific term based on its position. That is the functionality of recursive formulas. Therefore, it requires the previous term or terms to find the value of a specific term. To find a (3), we need the value of a (2) and to find the value a (2), we need the value of a(1). ![]() To find a (4), we need the value of a(3). Likewise, we can calculate the values of the terms in the sequence. Similarly, we can find the third term as follows. We can substitute value to the above formula. In a recursive formula, we can find the value of a specific term based on the previous term.įor example, assume a formula as follows. – Comparison of Key Differences Key Terms Difference Between Recursive and Explicit A formula describes a way of finding any term in the sequence. There are two types of formulas as recursive and explicit formulas. In other words, we can directly compute any term of the sequence using a formula. We can represent an arithmetic sequence using a formula. It refers to a set of numbers placed in order. Now finally, we can get our answer by adding 1 to both sides to get rid of the -1 on the right sideĪs you see, we're now left with n being the only number on one side of the equation and.The main difference between recursive and explicit is that a recursive formula gives the value of a specific term based on the previous term while an explicit formula gives the value of a specific term based on the position.Ī sequence is an important concept in mathematics. ![]() The identity property states that any number mutipled by 1 is that number Now to remove the -4 by dividing both sides by -4(making the -4 on the right side equal 1) We can do this by applying additive and subtractive properties of algebra: To do that, we'll isolate n so its the only term on a side of the equation and therefore making the other side of the equation the answer to n So since we already know the nth term as it was given to us, we can take the explicit formula: a(n) = 3 - 4(n-1) So the last question is a little tricky because it requires algebra = a ( 4 ) + 2 =a(4)+2 = a ( 4 ) + 2 equals, a, left parenthesis, 4, right parenthesis, plus, 2 = 9 =\goldD9 = 9 equals, start color #e07d10, 9, end color #e07d10Ī ( 5 ) a(5) a ( 5 ) a, left parenthesis, 5, right parenthesis = a ( 3 ) + 2 =a(3)+2 = a ( 3 ) + 2 equals, a, left parenthesis, 3, right parenthesis, plus, 2 = 7 =\greenD7 = 7 equals, start color #1fab54, 7, end color #1fab54Ī ( 4 ) a(4) a ( 4 ) a, left parenthesis, 4, right parenthesis = 5 + 2 =\purpleC5+2 = 5 + 2 equals, start color #aa87ff, 5, end color #aa87ff, plus, 2 = a ( 2 ) + 2 =a(2)+2 = a ( 2 ) + 2 equals, a, left parenthesis, 2, right parenthesis, plus, 2 = 5 =\purpleC5 = 5 equals, start color #aa87ff, 5, end color #aa87ffĪ ( 3 ) a(3) a ( 3 ) a, left parenthesis, 3, right parenthesis = 3 + 2 =\blueD3+2 = 3 + 2 equals, start color #11accd, 3, end color #11accd, plus, 2 = a ( 1 ) + 2 =a(1)+2 = a ( 1 ) + 2 equals, a, left parenthesis, 1, right parenthesis, plus, 2 = 3 =\blueD3 = 3 equals, start color #11accd, 3, end color #11accdĪ ( 2 ) a(2) a ( 2 ) a, left parenthesis, 2, right parenthesis ![]() = a ( n − 1 ) + 2 =a(n\!-\!\!1)+2 = a ( n − 1 ) + 2 equals, a, left parenthesis, n, minus, 1, right parenthesis, plus, 2Ī ( 1 ) a(1) a ( 1 ) a, left parenthesis, 1, right parenthesis A ( n ) a(n) a ( n ) a, left parenthesis, n, right parenthesis ![]()
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