Question

in an A. p., the mth term is 1/n and nth term is 1/m find the (MN) th term

Answer 1

let a be the first term and d the common difference. 

a + (m-1)d = 1/n.................(1) 

a + (n-1)d = 1/m.....................(2). 

subtracting (2) from (1), we get 

d(m-n) = 1/n - 1/m 

d(m-n) = (m-n) / mn 

d = 1/mn. 

sub this value of d in (1), 

a + (m-1)/mn = 1/n 

a = 1/n - (m-1)/mn 

= 1/mn. 


the starting term is 1/mn and the common difference is 1/mn. 

sum to mn terms = mn/2 * { 2a + (mn - 1)d } 

substituting the values of a and d, 

= mn/2 * {2/mn + (mn-1)/mn} 

= mn/2 * {2/mn - 1/mn + 1} 

= mn/2 * {1/mn + 1} 

= mn/2 * (mn + 1)/mn 


THIS IS UR ANS FRND.....

= 1/2 * (mn + 1)