For a given A.P.,the 5^{th} term is 20 and th | 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 $a_n = a + (n-1)d$.Given $a_5 = 20$,we have

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$730$

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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 $a_n = a + (n-1)d$.Given $a_5 = 20$,we have $a + 4d = 20$ (Equation $1$).Given $a_{10} = 35$,we have $a + 9d = 35$ (Equation $2$).Subtracting Equation $1$ from Equation $2$: $(a + 9d) - (a + 4d) = 35 - 20$,which gives $5d = 15$,so $d = 3$.Substituting $d = 3$ into Equation $1$: $a + 4(3) = 20$,so $a + 12 = 20$,which gives $a = 8$.The sum of the first $n$ terms is given by $S_n = \frac{n}{2} [2a + (n-1)d]$.For $n = 20$: $S_{20} = \frac{20}{2} [2(8) + (20-1)3]$.$S_{20} = 10 [16 + 19 	imes 3] = 10 [16 + 57] = 10 [73] = 730$.

For a given $A.P.$,the $5^{th}$ term is $20$ and the $10^{th}$ term is $35$. Find the sum of the first $20$ terms of this $A.P.$

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