For an A.P.,the 2^{nd} term is 2 and the 7^{t | vedclass

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(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.Given,the

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$1680$

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(B) Let the first term of the $A.P.$ be $a$ and the common difference be $d$.The $n^{th}$ term of an $A.P.$ is given by $a_n = a + (n - 1)d$.Given,the $2^{nd}$ term $a_2 = a + d = 2$  --- $(1)$.The $7^{th}$ term $a_7 = a + 6d = 22$ --- $(2)$.Subtracting equation $(1)$ from equation $(2)$:$(a + 6d) - (a + d) = 22 - 2$$5d = 20$$d = 4$.Substituting $d = 4$ in equation $(1)$:$a + 4 = 2$$a = -2$.The sum of the first $n$ terms is given by $S_n = \frac{n}{2} [2a + (n - 1)d]$.For $n = 30$:$S_{30} = \frac{30}{2} [2(-2) + (30 - 1)4]$$S_{30} = 15 [-4 + 29 	imes 4]$$S_{30} = 15 [-4 + 116]$$S_{30} = 15 	imes 112 = 1680$.Thus,the sum of the first $30$ terms is $1680$.

For an $A.P.$,the $2^{nd}$ term is $2$ and the $7^{th}$ term is $22$. Find the sum of the first $30$ terms of the $A.P.$

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