The sixth term of an A.P. is 19 and its seven | 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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$107$

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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 sixth term $a_6 = 19$,so $a + 5d = 19$ (Equation $1$).Given,the seventeenth term $a_{17} = 41$,so $a + 16d = 41$ (Equation $2$).Subtracting Equation $1$ from Equation $2$:$(a + 16d) - (a + 5d) = 41 - 19$$11d = 22$$d = 2$.Substituting $d = 2$ in Equation $1$:$a + 5(2) = 19$$a + 10 = 19$$a = 9$.Now,find the $50^{th}$ term $a_{50}$:$a_{50} = a + (50 - 1)d$$a_{50} = 9 + 49(2)$$a_{50} = 9 + 98 = 107$.

The sixth term of an $A.P.$ is $19$ and its seventeenth term is $41$. Find the $50^{th}$ term of the $A.P.$

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