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# If the 7th term of an AP is 23 and the 12th term is 38, find the first term 'a' and common difference 'd'.

$(a)\;a=6,d=4\qquad(b)\;a=5,d=3\qquad(c)\;a=-5,d-3\qquad(d)\;a=-5,d=3$

Answer :$(b) a=5,\;d=3$
$Explanation : T_{n}\; of\; AP=a+(n-1)d$
$T_{7}=a+6d=23\qquad(1)$
$T_{17}=a+11d=38\qquad(2)$
Subtracting (1) from (2)
$T_{12}-T_{7}=5d=15$
$d=15/5=3$
Subtracting value d=3 in $T_{7}$
$T_{7}=23=A+6d=a+3*6$
a+18=23
a=23-18=5
$a=5\;d=3.$