\(\displaystyle a_1+a_2+a_3+ .. +a_{10} =235 \Rightarrow \dfrac{(a_1+a_{10})10}{2} =235 \Rightarrow (a_1+a_{10})\cdot5=235|_{:5}\Rightarrow a_1+a_{10} = 47

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\Rightarrow a_1+a_1+9d=47 \Rightarrow 2a_1=47-9d\ \ \ (1)\)

\(\displaystyle a_{11}+a_{12}+a_{13}+ .. +a_{20} =735 \Rightarrow \dfrac{(a_{11}+a_{20})10}{2} =735 \Rightarrow (a_{11}+a_{20})\cdot5=735|_{:5}\Rightarrow a_{11}+a_{20} =1 47

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\Rightarrow a_1+10d+a_1+19d=147 \Rightarrow 2a_1=147-29d\ \ \ (2)\)

\(\displaystyle (1), (2) \Rightarrow 47-9d=147-29d \Rightarrow 29d-9d=147-47 \Rightarrow 20d=100\Rightarrow d=5\ \ \ (3)

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(1), (3) \Rightarrow 2a_1=47-9\cdot5 \Rightarrow 2a_1=2 \Rightarrow a_1=1.

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So,\ a_1=1,\ \ d=5 .\)

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