Question

Write three rational numbers between 3/4and 8/9such that the difference between thesuccessive numbers is the same. Obtain a general formula for n such numbersbetween 0 and 1. What can be the maximum value of n in the formula? Justify youranswer.​

Answer 1

Our three rational number are :-

=(3/4+8/9)/2

=(3*9 + 8* 4)/36*2

=(27 + 32) /36*2

=59/72-------------1st rational no.

(8/9+59/72)/2

(8*8+59*2)/72*2

(64+108)/144

172/144----------2nd rational no.

(59/72 + 3/4)/2

(59+3*8) /72* 2

(59+24)/144

(83)/144

83/144------------3rd rational no