For each of the following $A.P.s$,find the $n^{th}$ term: $27, 22, 17, 12, \ldots$
(N/A) The given arithmetic progression is $27, 22, 17, 12, \ldots$
Here,the first term $a = 27$.
The common difference $d = 22 - 27 = -5$.
The formula for the $n^{th}$ term of an $A.P.$ is $T_n = a + (n - 1)d$.
Substituting the values,we get $T_n = 27 + (n - 1)(-5)$.
$T_n = 27 - 5n + 5$.
$T_n = -5n + 32$.
Here,the first term $a = 27$.
The common difference $d = 22 - 27 = -5$.
The formula for the $n^{th}$ term of an $A.P.$ is $T_n = a + (n - 1)d$.
Substituting the values,we get $T_n = 27 + (n - 1)(-5)$.
$T_n = 27 - 5n + 5$.
$T_n = -5n + 32$.
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