If the 9^{th} term of an A.P. is 99 and 99^{t | vedclass

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(A) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The formula for the $n^{th}$ term of an $A.P.$ is $a_n = a + (n - 1)d.$Giv

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$0$

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(A) Let $a$ be the first term and $d$ be the common difference of the $A.P.$The formula for the $n^{th}$ term of an $A.P.$ is $a_n = a + (n - 1)d.$Given that the $9^{th}$ term is $99$:$a + 8d = 99$ $...(1)$Given that the $99^{th}$ term is $9$:$a + 98d = 9$ $...(2)$Subtracting equation $(1)$ from equation $(2)$:$(a + 98d) - (a + 8d) = 9 - 99$$90d = -90$$d = -1$Substituting $d = -1$ into equation $(1)$:$a + 8(-1) = 99$$a - 8 = 99$$a = 107$Now,find the $108^{th}$ term $(a_{108})$:$a_{108} = a + (108 - 1)d$$a_{108} = 107 + 107(-1)$$a_{108} = 107 - 107 = 0$Thus,the $108^{th}$ term is $0$.

If the $9^{th}$ term of an $A.P.$ is $99$ and $99^{th}$ term is $9,$ find the $108^{th}$ term.

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