Finding the nth term of a sequence is easy given a general equation. But doing it the other way around is a struggle. Finding a general equation for a given sequence requires a lot of thinking and practice, but learning the specific rule guides you in discovering the general equation. In ...
百度试题 结果1 题目 In the following exercises, find a general term for the sequence whose first five terms are shown. 相关知识点: 试题来源: 解析 a_n=e^(n+2) 反馈 收藏
a and Ban+1-α=kan-a(46.5.3)an+1-Ban-Bwhere k is contant and k =rpo≠0.r-pBThe general term of (46.5. 1)(the characteristic e-quation has two distinct roots a and B).Letaa(n-α)/(-β) (46.5.3)becomesSoa-a=b1k1(46.5.4)an-BSolving for ana_n=(βb_1k^(n-...
(3) Determine whether −15 is a term of the sequence. Explain your answer. 相关知识点: 试题来源: 解析 (1) a13=10−3(13) =10−39=−29 (2) If an=−71 10−3n=−71 −3n=−81 n=27 (3) If −15 is a term of the sequence, we let an=−15. Then, 10−...
The general term of an of a sequence is −3n+4. (1) Find the 3rd term of the sequence. (2) If ar−a3=−12, find the value of r. 相关知识点: 试题来源: 解析 (1) a3=−3(3)+4 =−5 (2) (−3r+4)−(−5)=−12 r=7 (1)略(2)略...
【解析】Su m:2/(3^n-1)The given recurrence relation can be expressed as1=3+1.an+1anL b_n=1/(a_n) Wehav b. =3b_n+1 , whhiteform of (46.2. 1).By (46.2.2), winb_1=1 , p=3 and q=1,we haveb_n=(b_1-q/(1-p))p^(n-1)+q/(1-p)=3^nc^n=(3^n-1...
百度试题 结果1 题目Find the general term, u_n, of the geometric sequence that has:u_2=-12 and u_7=512 相关知识点: 试题来源: 解析 u_n=18(-4)^(n-1) 反馈 收藏
百度试题 结果1 题目If the general term of a sequence is given by Tn=5−n3n, find the value of T2−T6 相关知识点: 试题来源: 解析 59 反馈 收藏
百度试题 结果1 题目Find the general term u_n of the geometric sequence which has:u_2=10 and u_4=250 相关知识点: 试题来源: 解析 u_n=2*5^(n-1) 反馈 收藏
解析 Solution: (A). The general term of the sequence can be written as: a_n=2/(n(n+1)) which can be decomposed into two parts a_n=2(1/n-1/(n+1)) . Let n =1,2,3,… S_n=2(1-1/2+1/2-1/3+⋯+1/n-1/(n+1)) =2(1-1/(n+1))=(2n)/(n+1) ...