For an A.P.,five times the 5^{th} term is equ | vedclass

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(A) 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 $a_n = a + (n - 1)d$.According

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$0$

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(A) 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 $a_n = a + (n - 1)d$.According to the problem,$5 	imes a_5 = 8 	imes a_8$.Substituting the formula for the terms: $5(a + 4d) = 8(a + 7d)$.Expanding the equation: $5a + 20d = 8a + 56d$.Rearranging the terms: $5a - 8a = 56d - 20d$.$-3a = 36d$,which simplifies to $a = -12d$.We need to find the $13^{th}$ term,$a_{13} = a + 12d$.Substituting $a = -12d$ into the expression for $a_{13}$:$a_{13} = -12d + 12d = 0$.Therefore,the $13^{th}$ term of the $A.P.$ is $0$.

For an $A.P.$,five times the $5^{th}$ term is equal to eight times the $8^{th}$ term. Find the $13^{th}$ term of the $A.P.$

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