1.Find an explicit formula for the general term of the given sequence:5, 10, 20, 40, 80,·…2.Find recursive formulas for the general term of the given sequences:5, 10, 20, 40, 80,· ..3.Write using summation notation: Ea,k=15+10+20+40+ 80+……+2560

Name: 1.Find an explicit formula for the general term of the given sequence
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: 1.Find an explicit formula for the general term of the given sequence:5, 10, 20, 40, 80,·…2.Find recursive formulas for the general term of the given sequences:5, 10, 20, 40, 80,· ..3.Write using summation notation: Ea,k=15+10+20+40+ 80+……+2560

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question. 1) The nth term of a geometric sequence is given by an=arn-1 where a is the first term and r is the common ratio. The given sequence is 5,10,20,40,80,…. Examine the common ratio of consecutive terms as follows. a2a1=105=2a3a2=2010=2a4a3=4020=2⋮ Observe that the common ration of every two consecutive terms is same. Thus, the given sequence is a geometric sequence with common ration r=2. Evaluate the nth term of the given sequence as follows. an=arn-1an=52n-1 Therefore, the n th term or general term of the given sequence is an=52n-1.