Question

in an A.P.if mth term is n and nth term is m,where m unequal to n, find the pth term

Answer 1

hello dear,

am = a+ (m-1)d = n ................(1)

an = a+(n-1)d = m ..............(2)

on substracting 1 and 2 ,

a +(m-1) d - a - (n-1)d = n -m

(m - 1 - n +1) d = n -m

(m-n) d = n-m

d = - (m-n) / m-n = -1

in equation 1 ,

a+(m-1)(-1) = n

a - m +1 = n

a = n+m -1

ap = a+(p-1)d

= n +m - 1 + (p-1)(-1)

= n+m -1 -p +1

= n+m -p

i hope its help you :-)

Answer 2

Answer:

The $p_{th}$ term is n+m-p

Step-by-step explanation:

As per the data given in the question,

we have,

Formula of $n^{th}$ term,

$a_{m} = a+ (m-1)d = n ................(i)a_{n} = a+(n-1)d = m ..............(ii)$

substracting (i) and (ii),

$a +(m-1) d - a - (n-1)d = n -m\\(m - 1 - n +1) d = n -m\\(m-n) d = n-m\\d =\frac{n-m}{m-n} = -1$

putting in equation (i)

$a+(m-1)(-1) = na - m +1 = na = n+m -1$

Since we have the value of a and d, so

$a_{p} = a+(p-1)d= n +m - 1 + (p-1)(-1)= n+m -1 -p +1= n+m -p$

Hence, the $p_{th}$ term is n+m-p

#SPJ2