Question

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

Answer 1

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 $n=10$

$t_{10}=4p–3q+10(q–p)$

$=4p–3q+10q–10p$

$=7q–6p$