I was working on some series problems, when I encountered this as part of "Mental Aptitude Test". The a(1) is a real number represents 'a' suffix '1'. Any help is appreciated.

a(1) = 2
a(2) = 3
a(r+2) = [5/a(r)] + a(r+1)
Find a(50) x a(51)

Question

I was working on some series problems, when I encountered this as part of "Mental Aptitude Test". The a(1) is a real number represents 'a' suffix '1'. Any help is appreciated.

a(1) = 2
a(2) = 3
a(r+2) = [5/a(r)] + a(r+1)
Find a(50) x a(51)

karim728 · Answer

geometric series?

jbedu · Answer

Not sure if it is GP. I thought the product of 2 consecutive number should be in AP. But I may be wrong, as I could not proceed further.

karim728 · Answer

i dont get this a(r+2) = [5/a(r)] + a(r+1)

jbedu · Answer

It means :
$$a_{r+2} = \frac{ 5 }{ a _{r} } + a _{r+1}$$

holsteremission · Answer

Just out of curiosity, are you sure it's not
$$a_{r+2}=\frac{5}{a_{r+1}}+a_r~?$$That appears to be much easier. Just making sure there's no typo.

jbedu · Answer

No its not, mate... If this is the case, its solvable ... it ends up as an AP with products of consecutive numbers. So the 50th term ($$a _{50} * a _{51}$$) equals to 251 as the initial number of the series will be 3 * 2 = 6.

It is possible that its a typo in the book itself. I plan to write to the publisher. Thanks mate.