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...
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 ...
Find the value of the limits of the recursive sequence defined by a_1 = 1, a_{n + 1} = 3 - \frac{1}{a_n} . Write out the first four terms of the sequence. Determine whether the sequence is monotonic or not. Determine whether the sequence converges, and if so find...
2. Find the Fibonacci number when $n = 7$, using the recursive relation.Solution: The formula to calculate the Fibonacci number is: $F_{n} = F_{n\;-\;1} + F_{n\;-\;2}$Taking $F_{0} = 0$ and $F_{1} = 1$$F_{2} = 0 + 1 = 1,\; F_{3} = 1 + 1 = 2,\...
The recursive formula of an arithmetic sequence:an=an−1+d, n≥2 and The sum of the first n terms of an arithmetic sequence:Sn=n2[2a+(n−1)d]Answer and Explanation: Given: The first term of the sequence a1=−4910 ...
Either the explicit or the recursive form may be used to describe an arithmetic sequence in which the first term is known. Practice using both of them on the examples in this section.Example: Writing a Recursive Formula for an Arithmetic Sequence Write a recursive formula for the arithmetic seq...
Suppose we are asked to find the first four terms of the sequence defined by the recursive formula 𝑇=𝑇+1,𝑇=10. We already know the first term, which is 𝑇=10. To find the second term, 𝑇, we substitute 𝑛=1 into the recursive formula 𝑇=𝑇...
Because each recursive sequence has a different starting term and a different "rule" by which the next term is found by the previous term or terms, there is not a single recursive formula. Each formula has to be found for each different sequence. A sequence could be written in general as...
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+...
What is the formula for t_(11) if the sequence 1, 3, 12, 60, ... is defined recursively and given that t_1=1? A: t_n=(t_(n-1))(n+1) B: t_n=(t_1)^nC: t_n=(t_(n-1))(n-1) D: t_n=(t_(n-1))(n) 相关知识点: 试题来源: 解析 ANone 反馈 收藏 ...