SOLUTION: Can someone show me how to work these? Find the 5th term for each: 1: A1=20, An=1/2A(n-1)+2 2: An=8n-5 3: A1=1/2, An=2A(n-1) I came up with 35 for #2, but I'm not even s

Algebra ->  Sequences-and-series -> SOLUTION: Can someone show me how to work these? Find the 5th term for each: 1: A1=20, An=1/2A(n-1)+2 2: An=8n-5 3: A1=1/2, An=2A(n-1) I came up with 35 for #2, but I'm not even s      Log On


   

Question 429511: Can someone show me how to work these?
Find the 5th term for each:
1: A1=20, An=1/2A(n-1)+2
2: An=8n-5
3: A1=1/2, An=2A(n-1)
I came up with 35 for #2, but I'm not even sure that's right. These are confusing me!
Thanks!
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
you are correct for number 2. Let's do problem 1 and then you can use the same process to do 3.
You are given
A%5Bn%5D+=+%281%2F2%29A%5Bn-1%5D+%2B2 and told A%5B1%5D=20
So now find A%5B2%5D
Plug in 2 for n in the given forumula
A%5B2%5D+=+%281%2F2%29A%5B2-1%5D+%2B2+
A%5B2%5D+=+%281%2F2%29A%5B1%5D+%2B2+
Now you see this formula contains A%5B1%5D which you know is 20. So subsitute 20 and solve
A%5B2%5D+=+%281%2F2%2920+%2B2+
A%5B2%5D+=+10+%2B2+
A%5B2%5D+=+12+
Now you have A%5B2%5D. So now solve for when n=3
A%5B3%5D+=+%281%2F2%29A%5B3-1%5D+%2B2+
A%5B3%5D+=+%281%2F2%29A%5B2%5D+%2B2+ you know A%5B2%5D because you just solved for it above. Plug 12 in for A%5B2%5D and solve for A%5B3%5D
A%5B3%5D+=+%281%2F2%2912+%2B2+
A%5B3%5D+=+6+%2B2+
A%5B3%5D+=+8+
Keep doing this process for n = 4 and then again for n=5.
A%5B4%5D+=+%281%2F2%298+%2B2+=+6
A%5B5%5D+=+%281%2F2%296+%2B2+=+5
Use the same process for problem 3