In an A.P., if mth term is n and the nth term is m, where m ≠ n, then find its pth term.

Question

In an A.P., if mth term is n and the nth term is m, where m ≠ n, then find its pth term. (A)  n - m + p (B) n + m + p  (C) n + m -p (D)  n - m - p

Tardigrade Admin · Accepted Answer

We have, am = a + (m - 1)d = n ....(i) and an = a + (n - 1)d = m ....(ii) Solving (i) and (ii), we get (m - n)d = n-m ⇒ d = -1 and so, a = n + m - 1 Now, ap = a + (p-1)d = n + m- 1 + (p- 1)(-1) = n + m -p

Q. In an $A . P$ ., if $m^{t h}$ term is $n$ and the $n^{t h}$ term is $m$ , where $m \neq = n$ , then find its $p^{t h}$ term.

$n - m + p$

$n + m + p$

$n + m - p$

$n - m - p$

We have, $a_{m} = a + (m - 1) d = n .... (i)$
and $a_{n} = a + (n - 1) d = m .... (ii)$
Solving $(i)$ and $(ii)$ , we get
$(m - n) d = n - m$
$\Rightarrow d = - 1$
and so, $a = n + m - 1$
Now, $a_{p} = a + (p - 1) d$
$= n + m - 1 + (p - 1) (- 1)$
$= n + m - p$

Q. In an A.P., if mth term is n and the nth term is m, where m=n, then find its pth term.

n−m+p

n+m+p

n+m−p

n−m−p