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Question

The third of an A.P is p and fourth term is q. Find the tenth term and the general term.

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Solution

Given t3=p and t4=q

nth term or general term of AP is tn=a+(n1)d

t3=a+2d=p... (1)

t4=a+3d=q... (2)

Subtract (1) from (2), we get

d=qp

Put value of d in (1), we get

a+2(qp)=p

a=p2q+2p=3p2q

General term, tn=(3p2q)+(n1)(qp)

=3p2qq+p+n(qp)

tn=4p3q+n(qp)

Put n=10

t10=4p3q+10(qp)

=4p3q+10q10p

=7q6p

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