Question

In an A.P if mth term is n and the nth term is m, where m≠n, find the path term.​

Answer 1

$\huge{\underline{\underline{\orange{Solution}}}}$

We have

↬ $a_m = a + (m - 1)d = n$⠀⠀⠀...1

↬ $a_n = a + (n - 1)d = m$⠀⠀⠀...2

★ Solving (1) and (2), we get

➮ $(m - n)d = n - m$

➮ $d = -1$

and,

➮ $a = n + m - 1$

Therefore,

⟹⠀⠀⠀⠀⠀⠀$\large{a_p = a + (p - 1)d}$

⟹⠀$\large{a_p = n + m - 1 + (p - 1)(-1)}$

⟹⠀⠀⠀⠀⠀⠀$\large{a_p = n + m - p}$

Hence, the pth term is n + m -p.

Answer 2

Step-by-step explanation:

Solution

We have

↬ a_m = a + (m - 1)d = nam=a+(m−1)d=n ⠀⠀⠀...1

↬ a_n = a + (n - 1)d = man=a+(n−1)d=m ⠀⠀⠀...2

★ Solving (1) and (2), we get

➮ (m - n)d = n - m(m−n)d=n−m

➮ d = -1d=−1

and,

➮ a = n + m - 1a=n+m−1

Therefore,

⟹⠀⠀⠀⠀⠀⠀\large{a_p = a + (p - 1)d}ap=a+(p−1)d

⟹⠀\large{a_p = n + m - 1 + (p - 1)(-1)}ap=n+m−1+(p−1)(−1)

⟹⠀⠀⠀⠀⠀⠀\large{a_p = n + m - p}ap=n+m−p

Hence, the pth term is n + m -p.