In an ap if tp=q and tq+p=0 then tq=?
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7
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
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Answer:it's
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