Find the 31^{st} term of an AP whose 11^{th} | vedclass

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(A) Given that,$a_{11} = 38$$a_{16} = 73$We know that the $n^{th}$ term of an $AP$ is given by $a_n = a + (n - 1)d$.For the $11^{th}$ term: $a + 10d =

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$178$

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(A) Given that,$a_{11} = 38$$a_{16} = 73$We know that the $n^{th}$ term of an $AP$ is given by $a_n = a + (n - 1)d$.For the $11^{th}$ term: $a + 10d = 38$ $...(1)$For the $16^{th}$ term: $a + 15d = 73$ $...(2)$Subtracting equation $(1)$ from equation $(2)$:$(a + 15d) - (a + 10d) = 73 - 38$$5d = 35$$d = 7$Substituting $d = 7$ in equation $(1)$:$a + 10(7) = 38$$a + 70 = 38$$a = 38 - 70 = -32$Now,find the $31^{st}$ term:$a_{31} = a + (31 - 1)d$$a_{31} = -32 + 30(7)$$a_{31} = -32 + 210$$a_{31} = 178$Thus,the $31^{st}$ term is $178$.

Find the $31^{st}$ term of an $AP$ whose $11^{th}$ term is $38$ and the $16^{th}$ term is $73.$

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