The 10^{th} and 20^{th} terms of an A.P. are | vedclass

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(A) For the given $A.P.$,the $10^{th}$ term $T_{10} = 73$ and the $20^{th}$ term $T_{20} = 143$.Using the formula for the common difference $d = \frac

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$213$

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(A) For the given $A.P.$,the $10^{th}$ term $T_{10} = 73$ and the $20^{th}$ term $T_{20} = 143$.Using the formula for the common difference $d = \frac{T_m - T_n}{m - n}$,we get:$d = \frac{T_{20} - T_{10}}{20 - 10}$$d = \frac{143 - 73}{10} = \frac{70}{10} = 7$Now,using the formula $T_n = a + (n - 1)d$ for the $10^{th}$ term:$T_{10} = a + 9d$$73 = a + 9(7)$$73 = a + 63$$a = 10$Finally,the $30^{th}$ term $T_{30}$ is given by:$T_{30} = a + 29d$$T_{30} = 10 + 29(7)$$T_{30} = 10 + 203 = 213$Thus,the first term is $10$,the common difference is $7$,and the $30^{th}$ term is $213$.

The $10^{th}$ and $20^{th}$ terms of an $A.P.$ are $73$ and $143$ respectively. Find the first term,the common difference,and the $30^{th}$ term of the $A.P.$

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