Question

find the largest term of the HP whose first two terms are 2/5 and 12/23 urgent

Answer 1

if the he two term are HP are 2/5 and 12/23 
there for first term of the corresponding AP is a = 5/2 
and 2nd term of corresponding AP is 23/12
therefore 
common difference d= 23 12 - 5 2 = 23 - 30 12 = -7 12 
let the positive smallest term of AP be nth term.
therefore 5 2 + ( n - 1 ) * (-7 12 ) ≥ 0 - 7 12 *  ( n - 1 )≥ - 5 2 ( n - 1 ) ≤ 5 2 * 12 7 n - 1 ≤ 30 7 =  4 . 2  n - 1 = 4 [ since n is an integern = 1 + 4 = 5 ]
fifth term of AP = 52 + ( 5 - 1 ) * (-7 12 ) = 52 - 73 = 15 - 146 = 16 
largest term of HP = 5th term 
therefore fifth term of HP = 6 

hope this will help u