For a given A.P.,the 11^{th} term is 38 and t | vedclass

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(D) For the given $A.P.$,the $11^{th}$ term $T_{11} = 38$ and the $16^{th}$ term $T_{16} = 73$.For an $A.P.$,the common difference $d$ is given by:$d

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$178$

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(D) For the given $A.P.$,the $11^{th}$ term $T_{11} = 38$ and the $16^{th}$ term $T_{16} = 73$.For an $A.P.$,the common difference $d$ is given by:$d = \frac{T_{m} - T_{n}}{m - n}$Substituting $m = 16$ and $n = 11$:$d = \frac{T_{16} - T_{11}}{16 - 11} = \frac{73 - 38}{5} = \frac{35}{5} = 7$Now,using the formula for the $n^{th}$ term $T_{n} = a + (n - 1)d$:$T_{11} = a + 10d$$38 = a + 10(7)$$38 = a + 70$$a = 38 - 70 = -32$Finally,find the $31^{st}$ term $T_{31}$:$T_{31} = a + 30d$$T_{31} = -32 + 30(7)$$T_{31} = -32 + 210 = 178$Thus,the $31^{st}$ term of the $A.P.$ is $178$.

For a given $A.P.$,the $11^{th}$ term is $38$ and the $16^{th}$ term is $73$. Find the $31^{st}$ term of the $A.P.$

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