Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $1.4, 2.3, 3.2, 4.1, \dots$

(A) To determine if the sequence is an $A.P.$,we check the common difference $d$ between consecutive terms.
$d_1 = 2.3 - 1.4 = 0.9$
$d_2 = 3.2 - 2.3 = 0.9$
$d_3 = 4.1 - 3.2 = 0.9$
Since the common difference $d = 0.9$ is constant,the sequence is an $A.P.$
The $n^{th}$ term of an $A.P.$ is given by $T_n = a + (n - 1)d$,where $a = 1.4$ and $d = 0.9$.
$T_n = 1.4 + (n - 1)0.9$
$T_n = 1.4 + 0.9n - 0.9$
$T_n = 0.9n + 0.5$