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(C) Let $a$ be the first term and $d$ be the common difference of the given $A.P.$Second term,$a + d = 12$ .....$(1)$Sum of the first nine terms,$S_9

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$20$

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(C) Let $a$ be the first term and $d$ be the common difference of the given $A.P.$Second term,$a + d = 12$ .....$(1)$Sum of the first nine terms,$S_9 = \frac{9}{2}(2a + 8d) = 9(a + 4d)$.Given that $S_9$ is more than $200$ and less than $220$:$200 $200 Substituting the value of $(a + d)$ from equation $(1)$:$200 $200 Subtracting $108$ from all sides:$92 Since the terms are positive integers,$d$ must be an integer. The only integer satisfying $92 Substituting $d = 4$ into equation $(1)$:$a + 4 = 12 \Rightarrow a = 8$.The $4^{th}$ term is $a + 3d = 8 + 3(4) = 8 + 12 = 20$.

Given an $A.P.$ whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$,then its $4^{th}$ term is

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