For an A.P.,the 7^{th} term is -1 and the 16^ | vedclass

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(A) Let the first term be $a$ and the common difference be $d$. The $n^{th}$ term of an $A.P.$ is given by $T_n = a + (n - 1)d$.Given,$T_7 = a + 6d =

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$T_n = 2n - 15$

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(A) Let the first term be $a$ and the common difference be $d$. The $n^{th}$ term of an $A.P.$ is given by $T_n = a + (n - 1)d$.Given,$T_7 = a + 6d = -1$ (Equation $1$).Given,$T_{16} = a + 15d = 17$ (Equation $2$).Subtracting Equation $1$ from Equation $2$: $(a + 15d) - (a + 6d) = 17 - (-1)$.$9d = 18$,which gives $d = 2$.Substituting $d = 2$ into Equation $1$: $a + 6(2) = -1$.$a + 12 = -1$,so $a = -13$.The general term is $T_n = a + (n - 1)d = -13 + (n - 1)2$.$T_n = -13 + 2n - 2 = 2n - 15$.

For an $A.P.$,the $7^{th}$ term is $-1$ and the $16^{th}$ term is $17$. Find the general term of the $A.P.$

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