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(D) Given: First term $a = 2$,last term $l = 50$,and sum $S_n = 442$.The formula for the sum of an $A.P.$ is $S_n = \frac{n}{2}(a + l)$.Substituting t

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$3$

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(D) Given: First term $a = 2$,last term $l = 50$,and sum $S_n = 442$.The formula for the sum of an $A.P.$ is $S_n = \frac{n}{2}(a + l)$.Substituting the values: $442 = \frac{n}{2}(2 + 50)$.$442 = \frac{n}{2}(52) \implies 442 = 26n$.$n = \frac{442}{26} = 17$.Now,use the formula for the $n^{th}$ term: $a_n = a + (n - 1)d$.$50 = 2 + (17 - 1)d$.$50 - 2 = 16d$.$48 = 16d$.$d = \frac{48}{16} = 3$.Therefore,the common difference $d$ is $3$.

For a finite $A.P.$,the first term is $2$ and the last term is $50$. If the sum of all the terms is $442$,find the common difference $d$.

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