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(D) For the given $A.P.$,the common difference $d = 5$ and the $15^{th}$ term $T_{15} = 72$.The formula for the $n^{th}$ term of an $A.P.$ is $T_{n} =

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$247$

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(D) For the given $A.P.$,the common difference $d = 5$ and the $15^{th}$ term $T_{15} = 72$.The formula for the $n^{th}$ term of an $A.P.$ is $T_{n} = a + (n - 1)d$,where $a$ is the first term.Substituting the values for the $15^{th}$ term:$72 = a + (15 - 1) 	imes 5$$72 = a + 14 	imes 5$$72 = a + 70$$a = 72 - 70 = 2$Now,to find the $50^{th}$ term $(T_{50})$:$T_{50} = a + (50 - 1)d$$T_{50} = 2 + 49 	imes 5$$T_{50} = 2 + 245$$T_{50} = 247$Thus,the first term of the $A.P.$ is $2$ and the $50^{th}$ term is $247$.

For a given $A.P.$,the common difference is $5$ and its $15^{th}$ term is $72$. Find the first term of the $A.P.$ and its $50^{th}$ term.

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