Question

The third term of an A.P is P and the fourth term is Q find the 10th term and the general term

Answer 1

Heya buddy !

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

Answer 2

HI DEAR,
Here is ur answer...............
Acc. To The question...
third term=a3=a+2d=P  .................................................1.      {here d=common difference of the A.P and a is the first term of the A.P}
a4=a+3d=Q..................................................2.
a=Q-3d
put this in eq. 1
Q-3d+2d=P
-d=P-Q
d=Q-P
put value of this in eq 2.
a=Q-3(Q-P)
a=Q-3Q+3P
a=3P-2Q
 now,
the tenth term =a+9d
                      =3P-2Q+9(Q-P)
                       =3P-2Q+9Q-9P
                       =7Q-6P
general term=a+(n-1)d
                     =3P-2Q+(n-1)(Q-P)
                      3P-2Q+Qn-Pn-Q+P
                       =4P-Pn-3Q+Qn
                       =P(4-n)-Q(3-n)
HOPE IT HELPS UH......................................
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