SOLUTION: Write a formula for the nth term of the infinite sequence. Do not use a recursion formula. 1, 1/4,1/9,1/16/,1/25 show work

Algebra ->  Sequences-and-series -> SOLUTION: Write a formula for the nth term of the infinite sequence. Do not use a recursion formula. 1, 1/4,1/9,1/16/,1/25 show work       Log On


   

Question 475304: Write a formula for the nth term of the infinite sequence. Do not use a recursion formula.
1, 1/4,1/9,1/16/,1/25 show work
Found 3 solutions by robertb, ccs2011, richard1234:
Answer by robertb(5830) About Me  (Show Source):
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Well set up a table to relate n to An, when An refers to the nth term of the sequence.
n = 1, 2, 3, 4, 5 ... n
An = 1, 1/4, 1/9, 1/16, 1/25 ... ?
Now try to establish a pattern.
1%2F4+=+1%2F2%5E2+=+1%2Fn%5E2
1%2F9+=+1%2F3%5E2+=+1%2Fn%5E2
1%2F16+=+1%2F4%5E2+=+1%2Fn%5E2
1%2F25+=+1%2F5%5E2+=+1%2Fn%5E2
Notice how the relationship remains constant for each n.
Therefore, An+=+1%2Fn%5E2

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
, this is actually easier than trying to write a recursive formula. The recursive formula might look something like where .