SOLUTION: The first three terms of the finite sequence 1, 1/x, 2, y form an arithmetic sequence, while the last three terms form a geometric sequence find the values of x and y.
Algebra ->
Sequences-and-series
-> SOLUTION: The first three terms of the finite sequence 1, 1/x, 2, y form an arithmetic sequence, while the last three terms form a geometric sequence find the values of x and y.
Log On
Question 1167377: The first three terms of the finite sequence 1, 1/x, 2, y form an arithmetic sequence, while the last three terms form a geometric sequence find the values of x and y. Answer by ikleyn(52776) (Show Source):
Then the term is the arithmetic mean of its neighbors
= = , so x = .
Hence, the terms , 2 and y form a geometric progression.
Then the ratio of this progression is = and y = = .
ANSWER. x= , y= .
