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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

Grade:9

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
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
25757 Points
3 years ago
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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