Question

if x,4,y are successive terms in an arithmetic sequence and x,3,y are successive terms in a geometric sequence, calculate 1/x + 1/y.

Answer 1

1/x + 1/y = (x+y)/(xy)
now in AP ,, (x+y)/2 =4
and in GP ,, sqrt(xy) = 3
just substitute values..

Answer 2

Can you continue? I still am n't too sure

Answer 3

from my 1st eqn,, x+y = 4*2 =8
from my 2nd eqn,, xy = 3^2 =9
so (x+y)/xy = 8/9 <= your ans

Answer 4

ty.

Answer 5

Though, how did you get x+y and sqrt(xy) in the first place

Answer 6

its arthimetic annd geometric mean
if a,b,c are in AP,,then b=(a+c)/2
and if they are in GP,,then b = sqrt(ac)
these are some simple formullaes which can be proved easily..
note general terms of AP are a,a+d,a+2d ...
and of GP are a,ar, ar^2 ,ar^3 ...

Answer 7

I see. Thanks again.

Answer 8

Wait. Sorry to bother again. But how do you know x+y = 1/x and sqrt(xy) = 1/y?

Answer 9

nonono..
1/x and 1/y are not equal to x+y and sqrt(xy) respectively,,
but 1/x + 1/y = (x+y)/(xy)
just take LCM on LHS and do the simple maths..

Answer 10

Ok. Got it. I wasn't thinking hard enough >.<