For an A.P.,the 7^{th} term is 34 and the 13^ | vedclass

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

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$89$

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(D) The $n^{th}$ term of an $A.P.$ is given by the formula $a_n = a + (n - 1)d$,where $a$ is the first term and $d$ is the common difference.Given,$a_7 = 34$,so $a + 6d = 34$ (Equation $1$).Given,$a_{13} = 64$,so $a + 12d = 64$ (Equation $2$).Subtracting Equation $1$ from Equation $2$:$(a + 12d) - (a + 6d) = 64 - 34$$6d = 30$$d = 5$.Substituting $d = 5$ into Equation $1$:$a + 6(5) = 34$$a + 30 = 34$$a = 4$.Now,to find the $18^{th}$ term $(a_{18})$:$a_{18} = a + 17d$$a_{18} = 4 + 17(5)$$a_{18} = 4 + 85$$a_{18} = 89$.

For an $A.P.$,the $7^{th}$ term is $34$ and the $13^{th}$ term is $64$. Then,the $18^{th}$ term of the $A.P.$ is........

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