Question

If the mth term af an AP is 1/p andits pth term im 1/m ,show that its mpth term is 1

Answer 1

Hey

Given :-

mth term = 1/ p

=> a + ( m -1 ) d = 1 / p -------( i )


And ,

pth term = 1 / m

=> a + ( p - 1 ) d = 1 / m -------( ii )


Now ,

eq ( i ) - eq ( ii ) , we get ,

a + ( m - 1 ) d - a - ( p - 1 ) d = 1 / p - 1 / m

=> md - d - pd + d = m - p / pm

=> md - pd = m - p / pm

=> d ( m - p ) = m - p / pm

=> d = 1 / pm

So , d = 1 / pm

Now , putting the value of d in eq ( i ) ,

we get ,

a + ( m - 1 ) d = 1 / p

=> a + ( m - 1 ) 1 / pm = 1 / p

=> a + 1 / p - 1 / pm = 1 / p

=> a = 1 / p - 1 / p + 1 / pm

=> a = 1 / pm

So , a = 1 / pm



Now ,

pmth term = a + ( pm - 1 ) d

= 1 / pm + ( pm - 1 ) 1 / pm

= 1 / pm + 1 - 1 / pm

= 1


So ,

mpth term = 1


thanks :)