Question
In an A.P, if mth term is n and nth term is m, show that its rth term is (m + n – r)
Solution
For an A.P.
`t_m = n`
`=> a + (m - 1)d = n` .....(i)
And `t_n = m`
=> a + (n - 1)d = m .....(ii)
Substracting (i) from (ii) we get
(n - 1)d - (m - 1)d = m - n
=> d(n - m) = m - n
=> -d(n - m) = m - n
=> d = -1
Substituting d = -1 in equation (i) we get
a + (m - 1)(-1) = n
=> a - m + 1 = n
=> a = m + n -1
Now `t_r = a + (r - 1)d`
= (m + n - 1) + (r - 1)(-1)
= m + n - 1 - r + 1
= m + n - r
Is there an error in this question or solution?
Solution In an A.P, If Mth Term is N and Nth Term is M, Show that Its Rth Term is (M + N – R) Concept: Arithmetic Progression - Finding Their General Term.
