Question

in an ap if tp=q and tp+q =0 then tq=?

Answer 1

Given:

In an ap tp=q and tp+q =0

To find:

In an ap if tp=q and tp+q =0 then tq=?

Solution:

From  given, we have,

tp = q and tp+q = 0

To find the nth term we use the formula,

tn = a + (n - 1)d

⇒ tp = a + (p - 1)d = q ...(1)

tp+q = a + [(p + q) - 1]d = 0 ...(2)

⇒ a + [(p + q) - 1]d = 0

a + pd + qd - d = 0

a + pd - d = -qd

a + (p - 1)d = - qd

using (1), we have,

q = - qd

d = -1

again using (1), we have,

a + (p - 1)d = q

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

a + -p + 1 = q

a = p + q - 1

Tq = a + (q - 1)d

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

= p + q - 1 - q + 1

= p

∴ Tq = p