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Standard XII

Mathematics

nth Term of A.P

The mth term ...

Question

The mth term of A.P is n and its nth term is m. its pth term is

m + n + p

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m + n- p

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m - n + p

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None

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Solution

The correct option is B m + n- p
$a_{m} = a + (m - 1) d = n$
$a_{n} = a + (n - 1) d = m$
_
$(m - n) d = n - m$
_
$\Rightarrow d = - 1$
$a + (1 - m) = n$
$\Rightarrow a = m + n - 1$
$_{p} = a + (p - 1) d$
$= m + n - 1 + 1 - p$
$a_{p} = m + n - p$
$\Rightarrow (B)$ .

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The mth term of A.P is n and its nth term is m. its pth term is

The correct option is B m + n- pam=a+(m−1)d=nan=a+(n−1)d=m_________________(m−n)d=n−m_________________⇒d=−1a+(1−m)=n⇒a=m+n−1p=a+(p−1)d=m+n−1+1−pap=m+n−p⇒(B).

The correct option is B m + n- p
$a_{m} = a + (m - 1) d = n$
$a_{n} = a + (n - 1) d = m$
_
$(m - n) d = n - m$
_
$\Rightarrow d = - 1$
$a + (1 - m) = n$
$\Rightarrow a = m + n - 1$
$_{p} = a + (p - 1) d$
$= m + n - 1 + 1 - p$
$a_{p} = m + n - p$
$\Rightarrow (B)$ .