third term of an ap is p and fourth term is q then the 10 tern is

Question

Saurabh Koranglekar · Answer

Dear student A3 = p = a + 2d a is first term d is common difference d = (q-p) A4 = a + 3d = q a= 3p-2q A10 = a + 9d (3p-2q) +(q-p)9 = 7q -6p

Arun · Answer

Given t3 = p and t4 = q
nth term or general term of AP is tn = a + (n – 1)d
⇒ t3 = a + 2d = p → (1)
⇒ t4 = a + 3d = q → (2)
Subtract (1) from (2), we get
d = q – p
Put value of d in (1), we get
a + 2(q – p) = p
⇒ a = p – 2q + 2p = 3p – 2q
General term, tn = (3p – 2q) + (n – 1)(q – p)
= 3p – 2q – q + p + n(q – p)
tn = 4p – 3q + n(q – p)
Put n = 10 in tn
t10 = 4p – 3q + 10(q – p)
= 4p – 3q + 10q – 10p
= 7q – 6p

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third term of an ap is p and fourth term is q then the 10 tern is

third term of an ap is p and fourth term is q then the 10 tern is

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