Question

the pth term of an AP is c and the qth term is d, what is the rth term？

Answer 1

$\it\huge\mathbb{Answer :-}}}$]
$<b>$]
Nth term Tn = a + ( n-1) d, where, a= first term. d = common difference

Tp = a + (p-1)d = - q
$<u>$]
= a + pd - d = -q …………. (1)

T(p+q) = a + ( p+q-1)d = 0
$<u>$]
= a + pd + qd - d = 0 ………(2)

eq(1) - eq(2)

=> -qd = -q

=> d= 1

eq(1) =>

a + p - 1 = - q

=> a = -p - q +1

So, qth term =

Tq = a + ( q-1)d

By putting the value of a & d

= -p - q +1 + (q-1)

= -p -q +1 + q -1
$<u>$]
= -p

Answer 2

answer:− 
Nth term Tn = a + ( n-1) d so ,

a= first term

d = common diff.

Tp = a + (p-1)d = - q

= a + pd - d = -q --(1)

T(p+q) = a + ( p+q-1)d = 0

= a + pd + qd - d = 0 --(2)

equation (1) - equation (2)

= -qd = -q

= d= 1

eq(1) =

a + p - 1 = - q

=> a = -p - q +1

therefore qth term =

Tq = a + ( q-1)d

putting the value of a and d
= -p - q +1 + (q-1)
= -p -q +1 + q -1
= -p
HOPE IT HELPS YOU!!!