Question

In H.P if mth term is 'n' and nth term is ' m' then find (m + n)th term

Answer 1

$\huge \orange{Hey !!}$

Solution :-

In H.P

Tm = a + (m - 1) d = 1/n _______(1)

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

Substracting equation ( 2 ) from 1st

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

(m - n )d = (m - n) / mn

d = 1/mn

since ,

Tm = a + ( m - 1) 1/mn = 1/n

a = 1/n - (m - 1)/mn

a = m - m + 1/mn

a = 1/mn

.Now,

t ( m + n ) th term = a + ( m + n - 1) d

= 1/mn + (m + n - 1) / mn

t(m + n) th term = [m + n /mn ] Answer ✔

______________________________

$\boxed{hope \: it \: helps \: you}$

$\underline \red{Rajukumar111}$

Answer 2

here is your answer OK
in this attachment OK