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(A) The given $A.P.$ is $9, 12, 15, \ldots$Here,the first term $a = 9$ and the common difference $d = 12 - 9 = 3$.The formula for the $n^{th}$ term of

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$T_{16} = 54, T_n = 3n + 6$

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(A) The given $A.P.$ is $9, 12, 15, \ldots$Here,the first term $a = 9$ and the common difference $d = 12 - 9 = 3$.The formula for the $n^{th}$ term of an $A.P.$ is $T_n = a + (n - 1)d$.For the $n^{th}$ term: $T_n = 9 + (n - 1)3 = 9 + 3n - 3 = 3n + 6$.For the $16^{th}$ term: $T_{16} = 3(16) + 6 = 48 + 6 = 54$.Thus,the $16^{th}$ term is $54$ and the $n^{th}$ term is $3n + 6$.

Find the $16^{th}$ term and the $n^{th}$ term of the $A.P.$ $9, 12, 15, \ldots$

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