shashank.ism wrote:Let m be the largest positive term of an harmonic progression whose first two terms are 2/5 and 4/9.

A real number r satisfying m/2-1/n < r <= m+1/n, for every positive integer n, is best described by:
1 < r < 5
2 < r <= 4
1 < r <= 5
2 <= r <= 4
none of these

The 3rd term of the series will be 8/19.
4th term = 2(8/37) = 16/37
I find that the largest term is varying as the series progresses.
Can someone guide me as to how we have to choose the largest term???
In the 4 terms given it is varying as 0.4 , 0.44 , 0.421 ,0.432 and so on.

Anyways I think this is a "Challenge Problem" rather than a GMAT problem..

shashank.ism wrote:Let m be the largest positive term of an harmonic progression whose first two terms are 2/5 and 4/9.

A real number r satisfying m/2-1/n < r <= m+1/n, for every positive integer n, is best described by:
1 < r < 5
2 < r <= 4
1 < r <= 5
2 <= r <= 4
none of these

2.5, 2.25,......0.25,0.....

Will be the series of 1/a1, 1/a2.... (if a1, a2 are in HP=> 1/a1, 1/a2... are in HP)

The largest term = 1/0.25 = 4

2-1/n < r<= m+1/n

for n =1

1< r <=5

D

(Now please do not post follow up comments saying this is a good approach, thanks in advance)

harsh.champ wrote:

shashank.ism wrote:Let m be the largest positive term of an harmonic progression whose first two terms are 2/5 and 4/9.

A real number r satisfying m/2-1/n < r <= m+1/n, for every positive integer n, is best described by:
1 < r < 5
2 < r <= 4
1 < r <= 5
2 <= r <= 4
none of these

The 3rd term of the series will be 8/19.
4th term = 2(8/37) = 16/37
I find that the largest term is varying as the series progresses.
Can someone guide me as to how we have to choose the largest term???
In the 4 terms given it is varying as 0.4 , 0.44 , 0.421 ,0.432 and so on.

Anyways I think this is a "Challenge Problem" rather than a GMAT problem..

A sequence of numbers is said to form a harmonic progression if their reciprocals form an arithmetic progression.
Like if a, a+d, a+2d,...... is in AP . SO 1/a,1/(a+d), 1/(a+2d)........is in HP
so here u can see since 2/5 and 4/9 are in HP.... so calculating the cd of corresponding AP
9/4-5/2 = -1/4
so here u can see the term would gradually decrease and will give a -ve term after a few terms....
since reciprocal of -ve term is also -ve ..
so ultimately u will get a -ve term ..Here the question is talking about largest positive term....So u can now easily understand and calculate the thing....