Using the recursive formula, am+1=am−1⋅am2am−1−am=34m−5⋅34m−12⋅34m−5−34m−1 =(34m−5⋅34m−1)(4m−5)(4m−1)(2⋅34m−5−34m−1)(4m−5)(4m−1) =96(4m−1)−3(4m−5)=34(m+1)−1, so our induction is complete. ...
The first two equations are essentially stating that the term in the first position equals 0 and the term in the second position equals 1. The third equation is a recursive formula, which means that each number of the sequence is defined by using the preceding numbers. For example, to defin...
Write the first five terms of the sequence defined by the recursive formula a_n = 2(an - 1) + 3 with a_1 = -2. Calculate the first four terms of the sequence a_n = n + (n + 1) + (n + 2) + ... + (6n), starting with n = 1. ...
67. Consider the sequence defined by an=−6−8nan=−6−8n. Is an=−421an=−421 a term in the sequence? Verify the result. 68. What term in the sequence an=n2+4n+42(n+2)an=n2+4n+42(n+2) has the value 41?41? Verify the result. 69. Find a recursive formula for ...
The recursive formula for an arithmetic sequence is:\(a_1=-8a_n=a_(n-1)+3.What is the 3rd term in the sequence?OA.-5O B. -14OC.-24O D.-2 相关知识点: 试题来源: 解析 a_1=-8 a_n=a_(n-1)+3 n=2then a_2=a_2+3 =a_1+3 =—8+3 a2=—5 n-3 then a_3=a_2+...
Inthepreviousexample,wecameupwiththeseventhtermbylookingatthepatternandapplyingittothenextterminthesequence.Butwhatifweareaskedtofindthe150thterm?Today,wearegoingtolookat2waystowritearule(anequation)forfindingthenthterminaseries:closedformulaandrecursiveformula.ClosedorExplicitFormula Withaclosedformula,wedonotneed...
{eq}a_n = (n-1) d + a_1 {/eq} Here, d is the common difference. Explicit Geometric Formula {eq}a_n = a_1 r^{n-1} {/eq} Here, r is the common ratio. Fibonacci Sequence The Fibonacci Sequence, {eq}{f_n} {/eq}, is defined by the recursive formula {...
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Example 4: Writing a Recursive Formula for an Arithmetic Sequence Write a recursive formula for the arithmetic sequence. {−18,−7,4,15,26,…}{−18,−7,4,15,26,…} Solution The first term is given as −18−18 . The common difference can be found by subtracting the first te...