Question

Determine the A.P. whose fifth term is $5$ and seventh term is $9$.

Answer 1

Formula,

$T_n=a+(n-1)d$

$T_5=a+(5-1)d=a+4d=5$.....(1)

$T_7=a+(7-1)d=a+6d=9$......(2)

(2)-(1) gives $d=2$

substitute the value of d in equation (1), we get, $a=5-4\times 2=-3$

The A.P series is $-3,-1,1,3,.....$